{ "cells": [ { "cell_type": "markdown", "id": "ee475a2c", "metadata": {}, "source": [ "# Relaxation Options" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "7897654e", "metadata": {}, "source": [ "SLEEPY has a variety of options for introducing relaxation to spin-systems. Understanding the differences between these can be important for correctly simulating complex effects. We explain and demonstrate the various options here. To keep things simple, we'll work with just single orientations.\n", "\n", "Most of the relaxation implemented in SLEEPY follows the Lindblad method of relaxation.$^1$ Note that we have implemented single-spin relaxation, which does not include singlet/triplet relaxation. This may be added in a future update.\n", "\n", "[1] C. Bengs, M.H. Levitt. [*J. Magn. Reson*](https://doi.org/10.1016/j.jmr.2019.106645), **2020**, 310, 106645." ] } , { "cell_type": "code", "execution_count": 0, "metadata": {"tags": [ "remove-cell" ]}, "outputs": [], "source": [ "# SETUP SLEEPY\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " !pip install sleepy-nmr" ] }, { "cell_type": "markdown", "id": "48d671c6", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2, "id": "58663ea4", "metadata": {}, "outputs": [], "source": [ "import SLEEPY as sl\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "6ad179c7", "metadata": {}, "source": [ "## Simple one-spin relaxation\n", "In the first example, we just introduce $T_1$ and $T_2$ relaxation along the *z*-axis and in the *xy*-plane, respectively." ] }, { "cell_type": "markdown", "id": "5bac6668", "metadata": {}, "source": [ "### Build the system" ] }, { "cell_type": "code", "execution_count": 3, "id": "82d4577a", "metadata": {}, "outputs": [], "source": [ "ex=sl.ExpSys(v0H=500,Nucs='1H',T_K=298)\n", "L=ex.Liouvillian()\n", "T1=1\n", "T2=0.1\n", "#Type of relaxation, spin-index, time constant\n", "L.add_relax('T1',i=0,T1=T1) \n", "_=L.add_relax('T2',i=0,T2=T2)" ] }, { "cell_type": "markdown", "id": "b6c5eecd", "metadata": {}, "source": [ "### Propagate" ] }, { "cell_type": "code", "execution_count": 4, "id": "ae6e88f7", "metadata": {}, "outputs": [], "source": [ "seq=L.Sequence(Dt=1e-3)\n", "rho=sl.Rho('1Hx+1Hz',['1Hx','1Hz'])\n", "_=rho.DetProp(seq,n=5000)" ] }, { "cell_type": "markdown", "id": "1fc4ea5d", "metadata": {}, "source": [ "### Plot the results" ] }, { "cell_type": "code", "execution_count": 5, "id": "8a32975a", "metadata": {}, "outputs": [ { "data": { "image/png": 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880+e9m2y+PquiGS7PivnZ5YFqFWrFm3btkVEqFOnDnFxcQAXZp4dPHgwXbp0oWXLlnnKa1fN6lan6XPTcFQue/WNlXKRS2vLzp07efXVVzl+/DjfffcdQJ5rS2bu/vfvsc1Lu3oVcUzfzsIdh7R58VJz58698NzPz++i5eDg4IuWw8LCLlouUaLERcu5nd593bp1DBgw4MJyt27d6NatG0ePHmXQoEG0b9+eli1bcvLkycve+/bbb9OuXbts9x0VFUV8fPyF5YSEBCIjI7Ndn5WAgIALzx0Ox4Vlh8NBWlrG3amrVq3KihUrmDVrFkOHDqV9+/Y8//zzOfwNeIbWdSvxy/p9nEs3+DiybgSV93Gn2lKxYkXGjRvH7bfffmFdXmtLZu7+9++xzUtYsB+F4xfw8YgveardZKvjKC+Snp7Otm3bqF69+mWvDR8+nMceewzI+9FR48aN2bZtG7t27aJMmTJMnjyZSZMmUa1atSzX59XevXspVqwYffr0ISQk5MIwuTepFHSand+/zY8tQrntxuZWx1Fe7kq1JbP8GHlx979/j73mBSAs+QB7Nq3mjF73olxo+/btREVFXTS6YYxh8ODBdOrUiQYNGuR4X7169eK6665jy5YtREVFMW7cOHx9fRk9ejQdOnSgRo0a3HHHHdSqVSvb9Xm1bt06mjRpQkxMDK+++irDhg3L877s6roqpUjasZQ/lq61OopSWdaWvMqqtmTm7n//ktV5cjtq1KiRWb58+UXr/tx0gPsnLuerB5pyfZUSFiVTrrJp0yZq1KhhdYwsjRo1iokTJ9K4cWNiYmLo16+f1ZHyTVa/dxFZYYyx3eRAWdWRG976k/IlQvj8viYWpVJWc+facvjwYZ599ll+//13+vbty9ChQ62OlCe5rSMee9oIoEnF4vg6hPnbD2nzoiz1xBNP8MQTT1gdQ+VB8yrh/LDyX1LPpePn49GD1cqGihcvzpgxY6yO4XIe/ZcYEuBL8OaZvPvfe62OopSyqfKOo2wf9xRf/Pib1VGUUk4e3bwAVI8K5zSB7D+mUwUopXKvfeMaCLBse+7ux6GUKjgefdoIYNjTA1ga3ITFu47RrX4hq+MopWymfOlwOj87jn2ecXmgUh7B40deakWGUTTYjz83Zn2nUeVZPOUCdLvwlt93q6rhrIk/QuJxHcH1Vt7y37oV8vK79fjmxcch+K6ayphHbyI9Pd3qOKoABQYGcvjwYS0yLmKM4fDhwwQGBlodpcBF+50kflQf3hn7ldVRlAW0thScvNYRjz9tBNAutiXbEs+wbs8h6kVHWB1HFZCoqCgSEhJITEy0OorXCAwMJCoqyuoYBa5jszqEVW9OQkqw1VGUBbS2FKy81BGvaF6euPcOvtlXgiV7Tmrz4sH8/PyoUKGC1TGUBwoM8OfOgcNZE38MY0y2c0Ypz6S1xf14/GkjgNJhQVQuEcTMf1ZYHUUpZVMtq4QTv3c/K7clWB1FKa/nFc0LwNnFk5j5Qh+OnjhldRSllA1VCUklYXQf3vnoM6ujKOX1vOK0EcA9d/Vmc0oxlu0+Svs6IVbHUUrZTONalajS9XGSIvI+X5RSKn+4fORFRDqKyBYR2S4iQ7J4PUxEZojIGhHZICL35cfn9u7UiqJ127Bk9+XThCul7MWqOtLrvofYnFSYs2nn8mN3Sqk8cmnzIiI+wIdAJ6Am0EtEal6y2WPARmNMPSAWeEdE/K/1s4P8fahXwsGUqd9e666UUhayso40r1iMo7vW8dPfev2cUlZy9chLE2C7MWanMSYFmAx0vWQbA4RKxuX8IcARIC0/Pjxg9yI2fPkic3V6e6XszLI6EhMZzMHJzzDqw4+vdVdKqWvg6mteygDxmZYTgKaXbDMamA7sBUKBO40xWd5dTkQeAh4CKFeu3FU/fODD9/LH0aJsTy5EbK6jK6XchGV1pGTxIrQd8D7JYVevN0qpguPqkZesbo5w6S0LOwCrgUggBhgtIoWz2pkxZqwxppExplF4ePhVP7xB9Whq1qnH3K2HchVaKeVWLK0jvbt1Iv6UEHdIpwpQyiqubl4SgLKZlqPIODLK7D5gmsmwHdgFVM+vAPWLpDDr83fZd+hofu1SKeValtaR2KrhnFr7GyM/n5Ifu1NK5YGrm5dlQBURqeC8eK4nGUO7me0B2gKISEmgGrAzvwJUCEzi6KLv+HLGX/m1S6WUa1laR6LDQ0ha+RM/fjc5P3anlMoDl17zYoxJE5H+wGzABxhvjNkgIv2cr48BXgEmiMg6MoaHBxtj8u08z/23d+LDtVM4FFopv3aplHIhd6gjT77zJVM3nODU2TRCArzmdllKuQ2X/9UZY2YBsy5ZNybT871A+4L6/KAAf9rUq8hfWxJJTzc4HDpHiVJ2Y3UdueW6mkxat5j52w7RsXapgvoYpVQ2vGZ6gMxqFjrDxi9e4Lvf/rE6ilLKhhqWL0rS0m8Z/srLVkdRyit5ZfPSrm40Z/dv47dlG62OopSyIT8fB0VSEtm0eTPp6Zd+0UkpVdC8snmpViGKm1+bxoEita2OopSyqdfeH0Nop/+yfu9xq6Mo5XW8snkBaF+rNOv+PU7CEb1Xg1Iq92KrRSACczYesDqKUl7Ha5uX68oGsnd8f4a88pbVUZRSNlQ8JIDANd8x/JE7rI6ilNfx2uYlplIZipevxu7kQKujKKVsqnGdqqSGRbHr4AmroyjlVby2eQEYOHwke4vW5ejpFKujKKVs6JWnn6B4+0f5Y4tOOaKUK3l189KhVinSUlL49h+dZVoplXvlixeieqlQflywzuooSnkVr25e6pQJI/HLAbz27CCroyilbCp4+xx+HtqdDTv2WB1FKa/h1c2LiNCpzyOkVbuRMylpVsdRStlQ3zu7UfSGB1i4S78yrZSreHXzAvDfR+7Ht1wM87bqOWulVO51ur4+tTr0YkF8ktVRlPIaXt+8NKlQjOCUo4ydNM3qKEopGxIR2lUtxu+zfyXh4GGr4yjlFby+efH1cSArp/LTe4M5nXTW6jhKKRuKStvH3ikvMHL8FKujKOUVvL55AXh68BBK3fUOS3YfszqKUsqG7unWnsp3vcrJkvWtjqKUV9DmBeh1YzOKR5Zn5tp9VkdRStmQr68PPbrfzD+7jpOUcs7qOEp5PG1eAH9fBw3DTjPxnRc4dlLnOlJK5d6NVYuyf+E0Rn75g9VRlPJ42rw41SycytFVs/ny53+sjqKUsqEWVUtxcsl3TP5OmxelCpqv1QHcRf8+3flyVxDbTEmroyilbMjfz5cnP/qJGVtOcepsGiEBWl6VKig68uIUFODPTQ2imbPpAMmpes5aKZV7d7asxdm0dP7YdMDqKEp5NG1eMrmutA+7vhjKqx9NtDqKUsqGGpYryrkV3zH4qf5WR1HKo2nzkkn7BlXwSU9hyfaDVkdRStmQwyFULOrPv4eOceyMzlavVEHR5iWTwAB/nho1mT1F6nH6rM51pJTKvZFvj6B4l0H8vlFPHSlVULR5ucQt9cqQlHKO7xdtsjqKUsqGYsoWIapoED8s3WF1FKU8ljYvl2hUvijHv3+BIf0ftDqKUsqGRIRS+xcx+cmObNu91+o4SnkkbV4u4XAIHbvfQVqF6zl4ItnqOEopG7rr5raENuzCb+u1eVGqIGjzkoVXn36M4Fpt+Gm1Fh6lVO51vaEZ1/V8gt/jdLJXpQqCNi9ZqBQeQq1wfz7+YrLVUZRSNtW9fiRLli1nwZotVkdRyuNo85KNov8uZNW4Z5nx9xKroyilbKhFGT/2fzGQF94YaXUUpTyO3r86Gy88+SB/JQaz7lQoN1sdRillO7Urlye2/5ucLFqZ9HSDwyFWR1LKY+jISzaqlI+kY9tYflqzl3Ppxuo4Sikbeur+nhw468vSuCNWR1HKo7i8eRGRjiKyRUS2i8iQbLaJFZHVIrJBRP52dcbzOlQtzJZZn/PJ1J+tiqCUsrH2NUuRHreMYa++bXUUpTyKS5sXEfEBPgQ6ATWBXiJS85JtigAfAbcYY2oBPVyZMbP2daI4tXImX/7wq1URlFJZsMtBUJC/D4UPrGL+9EmcTk61IoJSHsnVIy9NgO3GmJ3GmBRgMtD1km3+A0wzxuwBMMZYNtFQkdBC/G/8bxyufBNHT+s8JUq5A7sdBL3z7ruUvO8D5mzWOdOUyi+ubl7KAPGZlhOc6zKrChQVkbkiskJE7s5uZyLykIgsF5HliYmJBRAX7mpVg5Rz6fywKqFA9q+UyjVbHQTdWK8iUcVCmLos/uobK6VyxNXNS1aX2196Nawv0BC4CegAPCciVbPamTFmrDGmkTGmUXh4eP4mdaoZWZigjdMZ2Odm0tPTC+QzlFK5YquDIIdDaBJ8mG+H3sn8FRvyff9KeSNXNy8JQNlMy1HApbexTQB+NcacNsYcAuYB9VyUL0ut61fjXFgUS3foLLFKuQHbHQT1aReDI7AQUxfqhK9K5QdXNy/LgCoiUkFE/IGewPRLtvkJaCkiviISDDQFLP2Lf2vo40TdMoCf1h2yMoZSKoPtDoIa1qzCf4ZPZPGJIqSd0xFcpa6VS5sXY0wa0B+YTUZDMtUYs0FE+olIP+c2m4BfgbXAUuAzY8x6V+a8VGigH53rlOa7P5dx8MhxK6MopWx6ENSzcVkOHD3JlLmrrYyhlEfI0x12RaQRsNZ5sVyuGGNmAbMuWTfmkuW3gLfykq2gNAw9wbsfPsALRY/w8SuDrI6jlNcyxqSJyPmDIB9g/PmDIOfrY4wxm0Tk/EFQOm5wENSmWjiJXw1k6Jwoeq/+x8ooStlerpsXESkNLATuB77K90RuqmeHFrzU7XF2Bla2OopSHsHbDoL8fH249YEn+GNXMvuOJ1E6LMjqSErZVl5OG90DTAT65nMWt+ZwOHjmfwPZctKPNfHHrI6jlK1lOgi6w+osrvTawIcJKFeXqcv01gtKXYu8NC93AUMBfxGplM953NqtDcog+zcx8MU3rY6ilN155UFQueLBNIpw8N6773A2Re+4q1Re5ap5EZE2wGbn1fufAw8USCo3FRroR/EDy/l76ifsP3rK6jhK2ZnXHgTV8NnH7l8+YfSUWVffWCmVpdyOvDwAjHM+nwL0EBGvmpl69DsjiHxoLD+u1Xu+KJUX3n4Q9Gy/PsQMnMCK5JJWR1HKtnLceDjnCmkG/AJgjDkBLAY6F0gyN9WsZjTXVY3kq8W79X4NSuWNVx8EBQb48+DNLVi44zDbDpy0Oo5StpTjgmGMOWaMqWyMMZnW3WWMmVkw0dxX54p+LBv1KG+M/drqKErZih4EZejZuBzH//qMux9+3OooStnSNR3tOGd39To9WtYhwN+fORv11JFSuaEHQRmKFfKnfBE/tuw7xolkvXBXqdy61qHasc67VyIirfIhjy0EBwbw+vhp7CpUgy37ddhXqWshIl+ISJDzeRGL47jMV+M/pXCbB/luuX5tWqncutbm5XlgnIh8CTTOhzy20btpOQJ9YPhErzpgVKogOICPnQ3MQKvDuErtMmE0KFeEsT8vJi3tnNVxlLKVa21eXgG2kDGj69Rrj2MfRYL9KbH1J75+9m7Wb4+zOo5SdrYLeBH4GChkbRTXauC/lyUjevPGp5OsjqKUreSoeRGRqiKS1TT0TxtjXgQeAV7Iz2B28NrgJyhx8yB+3nra6ihKub0r1JFPjTFxZDQwHV0aymID+9xC2RvvZcnJolZHUcpWcjryMg04JiLLRGS8iDwlIm0BATDGnAYeLqiQ7qpVo9p0634b3yz/l6QUHfZV6iqyqyNJAMaYOGNMLWsjulZwYADPPzeMtUdEpx1RKhdy1LwYY2oDEcCjwM1AJeAZYJ2I7Hdu45X/976veXniF/zE/94cc/WNlfJiOakj3qhnk3L4HN7BY0NfsTqKUraRm/u8nDXGLANOGWMeN8a0NcaUAmoUXDz317RicdI3/8W33//AuXRz9Tco5cW0jlwuJMCXssfXsWjaZ2yM09svKJUTeblg96L/QxtjjuZTFltyOByM+fo7Ats/xc/r9lkdRym70DqSydi3XyH6sfFMWZNodRSlbCGnF+yOFpEHRKQ+zutc1P/r0bwGlSNCGPXrOs7plAFKZUnrSPaqlivFrU0qM3V5AodOJFkdRym3l9ORl7VAfWAkECoiG0XkWxF5SUTuLLB0NuFwCF2i0vjrpTt4bYxOGaBUNrSOXMHdTSLZNWEQdz0+xOooSrk935xsZIwZm3lZRKKAukAdoAsZk6t5tYe7tmREzeb8EZ/GMGPI+huhSnkvrSNXVqd8OBUqV2X9cV9OnU0jJCBH5Vkpr5Snm9QZYxKMMbOMMW8YY+7K71B2FBwYwDujxxBHBAt3HLY6jlJuT+vI5SZ/MR6f6jfwxaI4q6Mo5dZy3byIyOCCCOIJbm8YRVFHMgNeftfqKEq5Na0jWatXtgitqxTn7bFfc/DIMavjKOW2rtq8iMjUTI9vgb4uyGVLgX4+VDu5mmVfjmDK74utjqOU29A6knM3lkxi1zcvMuCVUVZHUcpt5eSk6gljzIVCIyIfF2Ae2/vwladZL+X4fofhjnZ67YtSTlpHcqhPlzaMf3Ikm4tUJynlHEH+PlZHUsrt5OS00auXLD9bEEE8RfEiofyv540sjTvCvK0HrY6jlLvQOpILI568i8NJaXyzdI/VUZRyS1dtXowxuwBEJFhE6hljjpx/TUTKiUiZggxoRz2blCV91TRuvakD6el63xeltI7kTpMKxSiftJWn7urK0ROnrI6jlNvJzQW7qcA0Eck8Zf1nQOn8jWR/Ab4+3NS0JimFSjJr1W6r4yjlTrSO5NB/mlch+cxpRs9YYnUUpdxObuY2SgV+AO6EjKMlINwYs7yAstnaqBcG0KDPED6cn0C6znmkFKB1JDcevrMLvV6fxHfbz3E8KdXqOEq5ldx+Vfoz4D7n87uBz/M3jufw83HwVLsqrN2wiRETfrA6jlLuROtIDj3dsTrHTp7mmY++tTqKUm4lV82LMWYzgIhUBXoBXxZEKE9xc91ITv36Hq8+O4iklDSr4yjlFrSO5FytyDAKr/mGj4fez5bde62Oo5TbyMsddseRceS01ttngr0aXx8Hoz76hGK3vcyXi/XaF6Uy0TqSQx++/jyle7zApNVHrr6xUl4iL83LVKAeGcVHXcU9XVrRtmFVPvhzu84Wq9T/0zqSQ60a1ebe27swaeke9hw+Y3UcpdxCrpsXY8wZY0yYMWZOXj5QRDqKyBYR2S4i2U6fKiKNReSciNyel89xJ0M6VmPn5Jfp0uchq6Mo5Ra0juTOE22rcGL5dDrc9h+royjlFvI0MWNeiYgP8CHQCagJ9BKRmtls9wYw25X5Ckr10mHUrlaZbaf82XXotNVxlLI1b6wjJQsH0qCUP7v3HmDh1v1Wx1HKci5tXoAmwHZjzE5jTAowGeiaxXaPA98DHnOL2hlffULJ63sw4pdNVkdRyu68so5898k71LtvOK/P3q63X1Bez9XNSxkgPtNygnPdBc47bXYHxlxtZyLykIgsF5HliYmJ+Ro0v0WEBvJI60r89MvvfPjNDKvjKGVn+VpH7KJQoB9DOlVn9dY4Xh0/zeo4SlnK1c1LVrMUXnoIMRIYbIw5d7WdGWPGGmMaGWMahYeH50e+AnVf83Ic/+1Dnn/xFc6mXfXHU0plLV/riJ0Ogm6pF8nZOaMYPuhRjp9OtjqOUpZxdfOSAJTNtBwFXHrzgkbAZBGJA24HPhKRbi5JV8BCggIY8+VUCnUZwrj5u6yOo5Rd5WsdsdNBkIgwetR7lLjjFcbOj7M6jlKWcXXzsgyoIiIVRMQf6AlMz7yBMaaCMSbaGBMNfAc8aoz50cU5C8w9nZrTsV45Rv2+hU279cI7pfLAq+vIHTe24I62Tfh03i627jtmdRylLOHS5sUYkwb0J+Pq/03AVGPMBhHpJyL9XJnFSsNuqs6eLwfTpUcfq6MoZTtaR2Bo5+ocnfs5rdvpzPXKO/m6+gONMbOAWZesy/KiOmPMva7I5Grliodwy609+GPXGf7emkjrqu49VK2Uu/H2OhIRGkiX62P4/s8Upq3Yze2NK1gdSSmXcvVpI+U08e1h1GnZiWE/ruOMznuklMqlz14fSpt7BjFi9g6ddVp5HW1eLBLg68OI2+qyad5MOt/zuNVxlFI24+MQXu1eh/1xW7jzieetjqOUS2nzYqEmFYpRwexj8YL5LNl+wOo4SimbqV0mjKiDi/n9mzH8s0Enf1XeQ5sXi/0y6VMa9HuPZ37aRHKq3vtFKZU73382kgZPfsbLs+O0hiivoc2LxUqEhTDi9npsS0jkkdfGWh1HKWUzZSKK8/Y9rdh64CRDxk6/+huU8gDavLiBVlXDidg+g4mvPMmfK7dYHUcpZTOtq4ZT5dB83n/8dr79bb7VcZQqcNq8uInvx7xNzb5vMfzPffrtI6VUro1/9b9Ed3mMsetSdPoR5fG0eXET5ctEMPZ/vdl1+DRPT/zL6jhKKZspVyqc8W8NY1tiEu/N3mh1HKUKlDYvbqR5pRK0DTvEh/06M/zjr6yOo5SymTbVImhbKoXn+rTnkyk/Wx1HqQKjzYubeffxHlSI7cHUPUEcPKmzxiqlcmd4n1hCI8ry4bw4jp/Rm9cpz6TNi5spXCiY2ZM+4axPMIOmrCZNz10rpXKhdImi/DnnN86EVeCZH9dhjLE6klL5TpsXN1SlZChPt6vAt6/359Z+T1sdRyllMzFli/BU20pM+uR9+r/0ntVxlMp32ry4qftaVSU6KpKFCcks3HHI6jhKKZt5qFUl/A9s4OuffmNH4imr4yiVr7R5cVMOh4Nlv02j3o09eOKbVRw4ode/KKVyzt/Pl4V/zSa62wAe/Wql3oJBeRRtXtxYSIAvH/dpyMEtq2jUpjPJZ1OsjqSUspFKpYszqlcDNu7czY33DCQ9Pd3qSErlC21e3FzVkqHcVj2I/XHbeG7yAqvjKKVsplXVcBqlbmDR92N5+7u/rY6jVL7Q5sUG3nv2cQaPnc63m84wdVm81XGUUjbz7ehXuW34ZD5dk8TKPUetjqPUNdPmxSZe7FaPFpWK8vATA/j021lWx1FK2Yivrw+f9b+JUmGB9Hx2NGu37rI6klLXRJsXm/D1cfB6l6qc3bGU5z78mvgjZ6yOpJSykbBgP97oXJEdU1/n5vufIilF7yGl7EubFxspV7oEixYtIiL2bh78Yjknk/XumUqpnGteO5qRE7+HZvcw6Ns1pKfrDeyUPWnzYjP1KpXhw94N2LRtJw069ODUGf0KtVIq5x7v2Ylnbq7HzFW7uf/F0VbHUSpPtHmxoZZVwrm1zGl2LpnDw6Nn6NGTUipXHmpVkej9fzPxlScZ9f2fVsdRKte0ebGp9555jBFT5rLgSDCvzdpkdRyllI2ICD+PHUHrp0YyakUyf29NtDqSUrmizYuNDbqlIfc2j2bkx5/R47FnrI6jlLKRkOBApr/+CFVKhnLfW1P4cvocqyMplWPavNiYiDDsphoUPbKBmbN+ZeL8HVZHUkrZSOFAPybc14iDs97n4X6PsO3ACasjKZUj2rzYnK+Pg9V/TufOZ0bxwszNfLNkt9WRlFI2UrJwEL9M/4HKvV/invHL+PdYktWRlLoqbV48QKGgAD657zpaRIfyQO8ePPHySKsjKaVspGXD2kx66iZOJKXS6q7/smLjNqsjKXVF2rx4iABfH0b/pwFhAcI3i3fy46p/rY6klLKR2mXCeLNTGeJ+m8itT7zC/uN6GwblvrR58SBFC4ewfcV82nX7DwOmruaT2autjqSUspHO19Xhu9l/U+i6nvzn08UcPKENjHJP2rx4mEKBfnx+X2MahCXzaLdW3P3061ZHUkrZSPfYRnzxQDMS9h+gdsuOrNqkXwRQ7sflzYuIdBSRLSKyXUSGZPF6bxFZ63wsFJF6rs5od4F+Pkx84iZqterMnydL8t7vWzFGb2SnlMqZRtHFGNKiKEe2r+aukTOIO3Ta6khKXcSlzYuI+AAfAp2AmkAvEal5yWa7gNbGmLrAK8BYV2b0FCHBgaz65Rt63dCQ9//YRvdBb5OUfNbqWErlCz0IKnj3d2/PglUb8Y+qxe1jFrFs216rIyl1gatHXpoA240xO40xKcBkoGvmDYwxC40xR52Li4EoF2f0GD4O4Y3b6nJTyRP89O7T3PDwi5w6m2Z1LKWuiR4EuU7TqpFMffg6Tu9cyXUxNflq5l9WR1IKcH3zUgaIz7Sc4FyXnQeAX7J7UUQeEpHlIrI8MVFvb50Vh0P4cEAvhrz/JQciW3DHmEUc0IvwlL3pQZALVY4IYeKAbhSv0oAX5x5m1rp9VkdSyuXNi2SxLsuLMUSkDRnNy+DsdmaMGWuMaWSMaRQeHp5PET3T60/0Ydy9TdiZsJ9qDa/n29nzrI6kVF7pQZCLNalTlY3zf6FuxdI88uUyHnj+fdLT062OpbyYq5uXBKBspuUo4LITqSJSF/gM6GqMOeyibB6vTbUI3uhcjuQj+/jvpKVMW5lgdSSl8kIPgixQPCSASQ82o/LxlYx/5Sl6v/I5KWnawChruLp5WQZUEZEKIuIP9ASmZ95ARMoB04C7jDFbXZzP43Vt05Rd27dwXfMWDJy6hvten8gZvZBX2YseBFkk0M+H3z9+nodeG8eipFLcPX4JiSd0OgHlei5tXowxaUB/YDawCZhqjNkgIv1EpJ9zs+eB4sBHIrJaRJa7MqM3KF00hK/6NqVbJV8mDHuAxrc/ysGTeh2Msg09CLKQw+Hgk6H38+4d9Vi8eiPR1Wox+Rc9Da1cy9fVH2iMmQXMumTdmEzP+wJ9XZ3L2/j5OBj5YAcCjn/MtANF6TTyH964tRbtakVaHU2pKzLGpInI+YMgH2D8+YMg5+tjuPggCCDNGNPIqsye6NYGUZju1blnui9DZ+4grWh5ejcth/P3rVSBEk+5eVmjRo3M8uU6SJMX2w6cpP/XK5j3wUCaNmnM7K8/IsDXx+pYysZEZIUdmwWtI7l35NRZBkxdw99bE6lxajUTX+5PRLEwq2MpD3ClOqLTAyiqlAzl24ebUrtGNdYd9+e2jxey/eApq2MppWygWEgA4+9tzO3R5/j1w+dofs9Q1iYcszqW8nDavCgAChcKYtmsb5j0zrMkHE2i9ePvcNsjQ0hJ1ZvaKaWuzMchvN3vFj797leKN+3KrR8t5LXvFmj9UAVGmxd1kQ61SvHbgFYUTlzHjO+n0OPj+ToKo5TKkb63tWf2wDbcUKUILzzckyotOhN/5IzVsZQH0uZFXSYiNJANc6by+Xcz2X0shY7v/sHt/Z/jxGktQkqpKysS7M+Ye5rxUP8BSLUb6DByHuP+2UGqjsKofKTNi8qSw+Ggd6ta/DagFZXObOb7D4fT+r+f8M82vQOpUurKHA4HH740kAUfPEnj6GL87+W3KFW9ASu3xV/9zUrlgDYv6ooiQgOZPWown/74B2GVYrhr3FJuGvQ+KzZuszqaUsrNlSkSxIT7GnNf27qkh4Rz5+frGDlnK0kpOgqjro02LypH+na9gV+fasXjrcsze8yLtOnRl3d/36qzVCulrkhEeGfIo2ydP4uOdUrzzowVhFesxZufT8NTbtWhXE+bF5VjgX4+/LdTbf7+ZwFd+w5i1B/baPHCD9z39Ks6xYBS6orCQwP4oFd93uhUHgfpjJy/j7vGLWXbgRNWR1M2pM2LyrUW9Wvy5YCb+eHR5rBtHhPeeYEbXvqOWev2kZ6uR1JKqez9p2NzDsdt5rX7O7M24RiNb7mXhp16sv+4zpGkck6bF5Vn9csVZdW37/PJ93MoVKIMj369kqqdH+CZdz/TJkYplS0/Xx/ubVGBvwbFUqN0YXYknib27bm88etmDh7TWzOoq9PmRV0Th8PBQ91i+W1Aa96+rSb71/7N6G9m0mHkPH5a/a/epEopla3iIQEs+nECa36dTIdapRg1bR5losry5LtfcTI51ep4yo1p86LyhY9DuL1xBY7s3sK4D95GBB55fxqFS5Zl2Kc/aiFSSmWrfIlCvN+zPmPvakhk1XpM2wUtRvzJsC//ZMeefVbHU25ImxeVr/z9fOnRrDK/PtmKoR2rUKR0eb7YcJbrXv+TJz6azuK1m62OqJRyUze1bMjulXOZNfhmrqtUnHeHD6N6nXq8MmMd+48nWx1PuRGdVVoVuDXxxxg3fxefDXuQlEN7uGfkDHpfF03rqhH4OMTqeKoA6KzSKj/8/PdSPv5pHhsDauAQodimH3iy73/ofVMbq6MpF7hSHdHmRbnMsvXbGDvjH1adK0fiyWSO//ASnbvexjvDnqR0WJDV8VQ+0uZF5af4I2f4YMZS3nm4C2HX96Zl97u5u2lZOtSMICQ40Op4qoBo86LcSuq5dH5cvJUnH76XlHJNKVyvPU2iQih+cAXPPHYPZSKKWx1RXSNtXlRBOHD4GDPW7mPSygOsX/gHR3/9gIff/ILHb2tDtVKhVsdT+exKdcTX1WGU8vNx0KNFdXqsX8yew2f4dkU8476eyqYvnmf6jrPc0rkDHaoU4YZakXpUpZS6oGTxIvRtU4T7W1dnbPmzvH94Lb8mCDNHziM8cSX1Ivx49/mBFA7ytzqqKmA68qLcQnp6Ol/8NIftpiSzNhxk15yvOLF0Gn1H/8zNjSvTumo4oYF+VsdUOaQjL8pVDp86yw+r/mXY4w9w9OBeyt8/khuqRVDdL5G7OrageBEdkbErPW2kbCX1XDoffTOTb2fO5kytbhw5ncKx3z6ieEA6w9//hLbVI4gorCMy7kybF+Vq6enpzFsfx9y4JGasjmf163cQWrUJdw95iy51S9MsOozChfTaOjvR5kXZ1rl0w/K4Iwx97gW2/nsI32Z3AZD6xygaNWnGoKf60zi6GIF+PhYnVZlp86KslJp2jjGTZ7D6YCorT4WRePAA+z59mNi+z/HwvX1oUz2C8NAAq2Oqq9BrXpRt+TiEphWL8+fXozHGsGnfSf7ctI/h048xf0Mca8YtJcDHkDz7Xbr2vJt77+hKnTJh+PnoLYyU8lZ+vj483qcb4PyCwPy1vLmzK4f9SvL092s5++9Gzs6fwGMvvssdbZtRM7Kw3rbBZrR5UbYhItSMLEzNyML037iEMylpLN55mBkL1jE2fgffzNvA9EPh+CYd5dTv79Or39PccdMNxJQtQpC/jswo5Y38fBz0aB1Dj9bfYIxh474TfPRVIt/MFyauPsGXm+aTvnUefgnLGTriA9rVLU/54sGIaDPjzvS0kfIYB08ks3z3UX6aM59v3nmWkBsfw79kZVLi13Lq78+58+k3adusAVWLB1AzqiiBAfqNhIKip42UHRw8mcyiHYcZ/eFHLJ79A8V6vYmIYFb/SJFzx3h6+Ns0Kl+MKhEhOHRkxuX0mhfllY4npbI87gjfzpzN9AkfUrTL/zgtQZxc+TNH/xpP5+Hf0ahGBcJSEgkPOEfXdtcTGqTnwfODNi/KbowxxB0+w/zth3jnlefYs2cPhW/6HwDHZr5FqZIRPPbMqzQsX5Qq4YGEh4VYnNjz6TUvyiuFBfnRtkZJ2ta4mzH/u/tCcZr68zlmFk7BP7QoU5fHk/DLGE6t/pVyA6cSXSIUn50LCEg+zOMDn6ZyRAhliwUR6Kd/Kkp5MhGhQolCVChRiLt+/gJjDLsPn2H57qO8tSmaI2l+vPP7VgD+HfMAJWs3p9ujw6hdJgw5uJWOzRtSvkyExT+F99CRF+XV0tMNSzdsY97ydQSUrcuWAyf46YMXSdy5nsj7RwNwaPob+KWe5pahH1OhRCFO71xBxdIluKVDG0oXDtTh5CzoyIvyRMfPpLJi92Hee/tNUkLLcKpUfeITjxL/3h2ENetBnW4PUaVEMHG/TaBL1+50aN2MSuEh+m3IPNKRF6Wy4XAIzepUpVmdqhfWfdR7BifPnGXXkSR2Jp7mq6S27Es8wuHTZ1ked4Ttn76CI6gwb6x6GX8fB0dnjCCiTHm6PDCIqKJB7N+wiJqVK9CmeSNKFg7UbzEo5SHCgv24oUYpbhj37oV1+4+eYlKdyRx3hHHIpwirN25h4befsfZUMKPWpHHuxEEOf/s8sfcOpk27dkQEpJOSGEe765sQXaq4XhicR9q8KJWF0OAA6gYHUDeqCN3qv3BhvTGGdX1+Y0v8IVJCIog/ksTXSyJIDyjEn1sOknjyLPGjnyS4UhOKd3oCX4ewf+JTlG90Ay1vf5CIwgGsnz2J+g0b06rl9ZQsHIBvymkqRpXE4dCvdytlN6WKhjDw3h6Z1jTg1LPd2ZV4kt3HU1mwcj1Tl1flUJo/Y/7eyamdqzg4ZRgle75GsSr1KXImgQPzvuHWfk/TsHYNCstZ/NNO0rReTUJ1epRs6WkjpfJRcuo5FqxYS+LpNExoSfYcPs0XbwwmrFIDCtVqw4Fjp1n3ShfCWvSiyPX/waSlsued7hRr1YeqHe8lzM+wdsIwGnbsScNWNxLim86GudO57vpW1K1dk8IBDkzySSpGlSLIjb8tpaeNlLpc6rl0Nu7ay+y58wktV5ODZ31Y+PefzP/iLcJ7vAShEZxaN4fDs0YS+dCnlIwqj8+/q0hc9gt3DBhO5XKlcJw6hJw5QmzL5pQuWohgf88dg9DTRkq5SKCfD22b1b9o3eBO0y9aPjroBPuPnuG08WXPwWN8l/Y8RaJrElymBHv3HyT59Em27z9K3IoEjhxIYO8nw5ix/klC6p4g9ehe9o59iOI3DSSiwY34nT7Ajq9fJOaOJ6lSvzmcOsTaWRNp3bU3VWvUgqQT7Fy7mOYtW1M2shQm9Sxnjh2iYnR5ioYGE+Tno9fsKOUifj4O6lWOol7lnv+/8uZa8PbjnEs37D2WxPL1kfzVLJpKTZtz4PQ55iec5dDe3czcdIQz649xbOFkjv/zFeX++wPi60fS8h84uWY2nV+aRERYMMc2L+Hk3u30fvhJwkMDST52kCBHOvVr16BwkJ/HnMZ2efMiIh2B9wEf4DNjzIhLXhfn652BM8C9xpiVrs6pVEEpWjiEooUzvmbZKLoYtzZ56eINHt9w4WnS2VS2DmhDiviT6ghk17/7+bXQi5Sr24zg8LLsiUvnVLmKhIQW5vDpFBK27WbdvNnsKxqDf5wPSbvXcHDys5Ts9RqB5eqStGslB6c+T8nebxEYVYOkHctI/OkNqvd9lxLR1UnavYadv4yj5YMvUjKqPMd3b2LrPzNo1+dxSoSHc3jPNravWkDbbr0oVrQoR/bt5t8dW2jZ9kYKFyrEyaOJnDiS6Mpfp1IewcchlC0WTNlW9eneKtMBUPc68MlzAJxITmXFhgqsWteVcnUakXjyLHOpxfpzh/H19WXL/pOs+f13jq77i3XhbQE4/OsHJG1fSlT/LxGBU3M/I/XATtoM+ogiQX7EL5yBSTpOt/sep3CQH3s2LifAAde3jqVwoB9Jxw5TNDSIspERBPi6z4XHLm1eRMQH+BC4EUgAlonIdGPMxkybdQKqOB9NgY+d/1TK6wQF+FGvWsULy80rl6B369qZtqgJj3XOtHw9jHoEYwzJqensP3Idmx+5kdDwUqT7BBKfEMmS2oWp3rgVPkGF2bHFsPBcT+o3rIpvSFG2HQ0iITCI5HRh9+EzxG3axo4Fv3O6xs2kFzrJkRW/cWT2aJY4auIbWpwTK2ZwdM4nRD3+NT7BYZxY+gNH/xpX4L8XPQhS3qhwoB9tGtakTcOaF9Y9EjsAGPD/G/03lhOnkziRYjh0KoUlTQLYvSeeyo1qcuxMCn8cr8u++DBCAnxJPHWWdauWcyoxgR1RHQA4MPV10pNPUfrujIuSD0x+FpOWQqk+b+Hv6+DgtOEEBATR+P4XCAnwZcMPH1GocBitejxIkJ8Pq36dTLHiJWjR/haC/H3YsOhPIsLDqd+4CUF+PuzdtY3wEsWoUL4sQX4+nEtJJiwkGP9c3o7Cpde8iMh1wIvGmA7O5aEAxpjXM23zCTDXGPONc3kLEGuM2Xelfeu5aqUKXkpqGsdOnsLhF0jKOcOBxEPs3hNPVMWqpBlhx44dbN64nuFPPVBg17w4D4K2kukgCOiV+SBIRDoDj5PRvDQF3jfGXPUgSOuI8lZn085xKjmNLTviOHriNEUjy3EqOY2/5/zG6eSzVGnShhPJqcz+6mPS8KHqjf/hZHIq8z8Zhk9wGFE39edMShpbPuqHb/GyhHcdDMC/n/QloEwNSnT5LwAJH91LYHQMJTo/BUD8B30IrnodJTv1J8DXwY4PH6BETFsqd7yPv5++wW2ueSkDxGdaTuDyUZWstikDXNa8iMhDwEMA5cqVy9egSqnL+fv5ElGsyIXlyCJlqV+l7IXlZhWLw41NGP7UAwUZowmw3RizE0BEJgNdgcwjuF2BL0zG0dliESkiIqWvdhCklLcK8PUhIMSH5vWqXbS+fa27L1oe2mnUxW/s9+fFyy/uIiU1jeRzhuSUc2zpMYc0HBQuUYqklHPMqzCKgNAilKlci+TUc/xy5nGKRUZTIaYiZ9PSmbGqDaWq1KF8VBH+vkJeVzcvWV0pdOnQT062yVhpzFhgLGQcMV1bNKWUTehBkFJuzN/PF3+/jNNcEQ1rXfTa9VV6XbR8b4uXL1p+rstXF56P/k/2n+HqG0skAGUzLUcBe/OwjVLKe+X7QZAxppExplF4ePg1h1NKFTxXNy/LgCoiUkFE/IGewPRLtpkO3C0ZmgHHdahXKZWJHgQp5eVc2rwYY9KA/sBsYBMw1RizQUT6iUg/52azgJ3AduBT4FFXZlRKuT09CFLKy7n8Pi/GmFlkNCiZ143J9NwAj7k6l1LKHowxaSJy/iDIBxh//iDI+foYMmpMZzIOgs4A91mVVymV//QOu0op29GDIKW8m84Ep5RSSilb0eZFKaWUUraizYtSSimlbMWl0wMUJBE5CWyxOkcelAAOWR0il+yYGTS3K1UzxoRaHSK3bFpH7PjfB2huV7JjZoDyxpgsb77kSRfsbimouVQKkogst1tuO2YGze1KImLXCYJsV0fs+N8HaG5XsmPmq9HTRkoppZSyFW1elFJKKWUrntS8jLU6QB7ZMbcdM4PmdiU7ZgZ75rZjZtDcrmTHzFfkMRfsKqWUUso7eNLIi1JKKaW8gDYvSimllLIVj2heRKSjiGwRke0iMsTqPOeJyHgROSgi6zOtKyYiv4vINuc/i2Z6bajzZ9giIh2sSQ0iUlZE/hKRTSKyQUSedPfsIhIoIktFZI0z80vunjlTDh8RWSUiM22UOU5E1onI6vNfi7ZD7uy4aw25kqzqix1kV1/cWXb1xS4urTEewRhj6wcZs8ruACoC/sAaoKbVuZzZWgENgPWZ1r0JDHE+HwK84Xxe05k9AKjg/Jl8LMpdGmjgfB4KbHXmc9vsgAAhzud+wBKgmTtnzpR9IDAJmGmj/0bigBKXrHP73Nn8LG5bQ66S+7L6YodHdvXF6lxXyZxlfbE6Vy7yX1RjPOHhCSMvTYDtxpidxpgUYDLQ1eJMABhj5gFHLlndFZjofD4R6JZp/WRjzFljzC5gOxk/m8sZY/YZY1Y6n58ENgFlcOPsJsMp56Kf82Fw48wAIhIF3AR8lmm1W2e+ArvmdtsaciXZ1Be3d4X64rauUF/cXjY1xvY8oXkpA8RnWk7Avf8QShpj9kHGHzEQ4Vzvlj+HiEQD9ck40nDr7M6h0dXAQeB3Y4zbZwZGAk8D6ZnWuXtmyCjcv4nIChF5yLnODrmz4u75PNYl9cWtZVNf7GAkl9cY2/OE5kWyWGeLjvgSbvdziEgI8D3wlDHmxJU2zWKdy7MbY84ZY2KAKKCJiNS+wuaWZxaRLsBBY8yKnL4li3VW/TfSwhjTAOgEPCYira6wrTvlzoq75/NIuagvbiGX9cUt5KHG2IYnNC8JQNlMy1HAXouy5MQBESkN4PznQed6t/o5RMSPjMLytTFmmnO1LbIbY44Bc4GOuHfmFsAtIhJHxqmKG0TkK9w7MwDGmL3Ofx4EfiDj1Ivb586Gu+fzONnUF1u4pL64u+xqjO15QvOyDKgiIhVExB/oCUy3ONOVTAfucT6/B/gp0/qeIhIgIhWAKsBSC/IhIgKMAzYZY97N9JLbZheRcBEp4nweBLQDNrtzZmPMUGNMlDEmmoz/bv80xvRx58wAIlJIRELPPwfaA+tx89xXYLcaYmtXqC9u6wr1xa1docbYn9VXDOfHA+hMxhXrO4Bnrc6TKdc3wD4glYyjuweA4sAfwDbnP4tl2v5Z58+wBehkYe7ryRg2Xwusdj46u3N2oC6wypl5PfC8c73bZr4kfyz//20jt85Mxrdy1jgfG87/zbl77qv8TG5ZQ66S+bL6YnWmHObOsr5YnesqmbOsL3Z6ZK4xnvDQ6QGUUkopZSuecNpIKaWUUl5EmxellFJK2Yo2L0oppZSyFW1elFJKKWUr2rwopZRSyla0eVEFQkSKiMijV9nmExFp4apMSil707qiztPmRRWUIsAViwzQFFhc8FGUUh6iCFpXFNq8qIIzAqgkIqtF5K1LXxSRGsBWY8y5S9ZPEJGPReQvEdkpIq1FZLyIbBKRCc5tfJzbrReRdSIywCU/kVLKanmtKz2c9WKNiMxzVVhVcHytDqA81hCgtsmYyCwrnYBfs3mtKHADcAswg4z5OfoCy0QkBvAByhhjakPGUHK+pVZKubO81pXngQ7GmH+1XngGHXlRVulA9s3LDJNx6+d1wAFjzDpjTDoZt6KPBnYCFUXkAxHpCLj9jLRKKZfIrq4sACaIyINkHPwom9PmRbmciAQDRYxzZuIsnHX+Mz3T8/PLvsaYo0A9MmZ2fQz4rICiKqVs4kp1xRjTDxhGxuzhq0WkuKvzqfylp41UQTkJhGbzWhvgr7zuWERKACnGmO9FZAcwIa/7UkrZSp7qiohUMsYsAZaIyM1kNDGHCyaicgUdeVEFwhhzGFjgvEju0gvrrnS9S06UAeaKyGoyGpeh17AvpZRNXENdect5cf96YB4ZM6IrG9NZpZXLichKoKkxJtXqLEopz6B1xbto86KUUkopW9HTRkoppZSyFW1elFJKKWUr2rwopZRSyla0eVFKKaWUrWjzopRSSilb0eZFKaWUUrbyfxq1Smf7EO59AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(det_num=0,ax=ax[0],axis='ms')\n", "ax[0].plot(rho.t_axis*1e3,np.exp(-rho.t_axis/T2),color='black',linestyle=':')\n", "ax[0].set_xlim([-1,500])\n", "ax[0].set_title(r'$T_2$ relaxation')\n", "ax[0].legend(('Simulation',rf'$T_2$={T2*1e3:.0f} ms'))\n", "rho.plot(det_num=1,axis='s',ax=ax[1])\n", "ax[1].plot(rho.t_axis,np.exp(-rho.t_axis/T1),color='black',linestyle=':')\n", "ax[1].set_xlim([0,rho.t_axis[-1]])\n", "ax[1].set_title(r'$T_1$ relaxation')\n", "_=ax[1].legend(('Simulation',rf'$T_1$={T1:.0f} s'))" ] }, { "cell_type": "markdown", "id": "5eb7d936", "metadata": {}, "source": [ "Not surprisingly, we obtain perfect monoexponential relaxation, matching the input rate constants for both $T_2$ and $T_1$.\n", "\n", "Note that $T_1$ relaxation as implemented in SLEEPY does not produce any $T_2$ relaxation. Caution should be taken to also include $T_2$ relaxation such that $2\\cdot T_1\\ge T_2$.$^2$\n", "\n", "[2] D.D. Traficante. [*Conc. Magn. Reson.*](https://doi.org/10.1002/cmr.1820030305), **1991**, 3, 171-177." ] }, { "cell_type": "markdown", "id": "70c59517", "metadata": {}, "source": [ "### Thermalization\n", "We may also force the magnetization to recover to its thermal equilibrium, by calling `L.add_relax('recovery')`. This function works by adding terms to all non-zero off-diagonal matrix elements of the relaxation matrix so that for the $\\alpha$ and $\\beta$ states of a spin, we have that \n", "\n", "$$\n", "\\begin{equation}\n", "\\frac{p_{eq}^\\alpha}{p_{eq}^\\beta}=\\frac{k_{\\beta\\rightarrow\\alpha}}{k_{\\alpha\\rightarrow\\beta}}\n", "\\end{equation}\n", "$$\n", "\n", "which satisfies [detailed balance](https://en.wikipedia.org/wiki/Detailed_balance). Note that we also add these terms to coherences, so that, for example, the $S^\\alpha I_x$ coherence transfers magnetization to the $S^\\beta I_x$ coherence more quickly than $S^\\beta I_x$ to $S^\\alpha I_x$. This occurs, even though both the coherences relax to zero. This is only relevant if the longitudinal relaxation of the *S*-spin is comparable to or faster than the transverse relaxation of the *I*-spin, a situation which arises primarily for electron-nuclear systems. We demonstrate recovery for one spin. To see how this influences relaxation of coherences, see the section on [contact shifts](../Chapter5/Ch5_ContactShift.ipynb)\n", "\n", "An important note: `L.add_relax('recovery')` should only be applied after all $T_1$ relaxation is introduced, since the adjustment to the relaxation matrix depends on what values of $T_1$ are used. Furthermore, the thermal equilibrium depends on the temperature setting of the experiment (an optional argument of ExpSys, which defaults to 298 (K))." ] }, { "cell_type": "markdown", "id": "e0f7e728", "metadata": {}, "source": [ "We now start the system without any longitudinal magnetization, since the system should recover to thermal equilibrium." ] }, { "cell_type": "code", "execution_count": 6, "id": "b8c1bae1", "metadata": {}, "outputs": [], "source": [ "L.add_relax('recovery')\n", "\n", "seq=L.Sequence(Dt=1e-3)\n", "rho=sl.Rho('1Hx',['1Hx','1Hz'])\n", "_=rho.DetProp(seq,n=5000)" ] }, { "cell_type": "code", "execution_count": 7, "id": "028cdef1", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(det_num=0,ax=ax[0],axis='ms')\n", "ax[0].plot(rho.t_axis*1e3,np.exp(-rho.t_axis/T2)*ex.Peq[0],color='black',linestyle=':')\n", "ax[0].set_xlim([-1,500])\n", "ax[0].set_title(r'$T_2$ relaxation')\n", "ax[0].legend(('Simulation',rf'$T_2$={T2*1e3:.0f} ms'))\n", "rho.plot(det_num=1,axis='s',ax=ax[1])\n", "ax[1].plot(rho.t_axis,(1-np.exp(-rho.t_axis/T1))*ex.Peq[0],color='black',linestyle=':')\n", "ax[1].set_xlim([0,rho.t_axis[-1]])\n", "ax[1].set_title(r'$T_1$ relaxation')\n", "_=ax[1].legend(('Simulation',rf'$T_1$={T1:.0f} s'))" ] }, { "cell_type": "markdown", "id": "f15624ac", "metadata": {}, "source": [ "Now, the longitudinal magnetization starts out at zero, and recovers to the thermal equilibrium, again yielding monoexponential functions matching the input relaxation times." ] }, { "cell_type": "markdown", "id": "98f06063", "metadata": {}, "source": [ "## Relaxation in a tilted frame" ] }, { "cell_type": "markdown", "id": "c4b16f92", "metadata": {}, "source": [ "The above relaxation methods can be applied to most spin-simulations. However, what happens if the quantization axis for a spin is tilted away from the z-axis? In this case we need to use more advanced options. We first demonstrate that the above approach fails with a tilted spin, by using a strong electron-nuclear hyperfine coupling and observing its influence on the nucleus.\n", "\n", "To obtain tilting of the nucleus, we need to calculate the nucleus in the lab frame. We leave the electron in the rotating frame." ] }, { "cell_type": "code", "execution_count": 17, "id": "cdfa8144", "metadata": {}, "outputs": [], "source": [ "# Don't forget to set vr to zero\n", "#It will default to 10 kHz if anisotropic interactions are present\n", "ex=sl.ExpSys(v0H=200,Nucs=['1H','e'],vr=0,LF=[True,False],T_K=298,pwdavg='alpha0beta45')\n", "ex.set_inter('hyperfine',i0=0,i1=1,Axx=-1e8,Ayy=-1e8,Azz=2e8)\n", "L=ex.Liouvillian()\n", "\n", "T1=1\n", "T2=0.1\n", "\n", "#Type of relaxation, spin-index, time constant\n", "L.add_relax('T1',i=0,T1=T1) \n", "_=L.add_relax('T2',i=0,T2=T2)" ] }, { "cell_type": "markdown", "id": "01774f97", "metadata": {}, "source": [ "### Tilted frame without thermalization" ] }, { "cell_type": "code", "execution_count": 18, "id": "bf5d76c7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->8\n" ] } ], "source": [ "seq=L.Sequence(Dt=1e-3)\n", "rho=sl.Rho('1Hx+1Hz',['1Hx','1Hz'])\n", "_=rho.DetProp(seq,n=5000)" ] }, { "cell_type": "code", "execution_count": 19, "id": "63ff2987", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(det_num=0,ax=ax[0],axis='ms')\n", "ax[0].plot(rho.t_axis*1e3,np.exp(-rho.t_axis/T2),color='black',linestyle=':')\n", "ax[0].set_xlim([-1,500])\n", "ax[0].set_title(r'$T_2$ relaxation')\n", "ax[0].legend(('Simulation',rf'$T_2$={T2*1e3:.0f} ms'))\n", "rho.plot(det_num=1,axis='s',ax=ax[1])\n", "ax[1].plot(rho.t_axis,np.exp(-rho.t_axis/T1),color='black',linestyle=':')\n", "ax[1].set_xlim([0,rho.t_axis[-1]])\n", "ax[1].set_title(r'$T_1$ relaxation')\n", "_=ax[1].legend(('Simulation',rf'$T_1$={T1:.0f} s'))" ] }, { "cell_type": "markdown", "id": "4469b7c8", "metadata": {}, "source": [ "The $T_2$ relaxation has a slow component, and the $T_1$ relaxation is too fast. This is because the nucleus is titled into the xy-plane, and so some $T_2$ relaxation is applied to the populations, accelerating its decay. Furthermore, parts of the coherences are relaxing with $T_1$.\n", "\n", "Note that this is signal in the lab frame. We could downmix it to detect in the rotating frame (`rho.downmix()`), but for our purposes, this is not really necessary." ] }, { "cell_type": "markdown", "id": "3d629364", "metadata": {}, "source": [ "### Tilted frame with thermalization\n", "Above, we see that the tilted frame distorts relaxation behavior using the basic SLEEPY settings. Here, we observe that it also causes thermalization to fail." ] }, { "cell_type": "code", "execution_count": 20, "id": "d20c36dc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->8\n" ] } ], "source": [ "L.add_relax('recovery')\n", "\n", "seq=L.Sequence(Dt=1e-3)\n", "rho=sl.Rho('1Hx',['1Hx','1Hz'])\n", "_=rho.DetProp(seq,n=15000)" ] }, { "cell_type": "markdown", "id": "bd052a0a", "metadata": {}, "source": [ "Mixing of $T_1$ and $T_2$ furthermore distorts the thermalization process, where $T_2$ relaxation destroys some of the thermal magnetization." ] }, { "cell_type": "code", "execution_count": 21, "id": "ff4ff5b4", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(det_num=0,ax=ax[0],axis='ms')\n", "ax[0].plot(rho.t_axis*1e3,np.exp(-rho.t_axis/T2)*ex.Peq[0],color='black',linestyle=':')\n", "ax[0].set_xlim([-1,500])\n", "ax[0].set_title(r'$T_2$ relaxation')\n", "ax[0].legend(('Simulation',rf'$T_2$={T2*1e3:.0f} ms'))\n", "rho.plot(det_num=1,axis='s',ax=ax[1])\n", "ax[1].plot(rho.t_axis,(1-np.exp(-rho.t_axis/T1))*ex.Peq[0],color='black',linestyle=':')\n", "ax[1].set_xlim([0,rho.t_axis[-1]])\n", "ax[1].set_title(r'$T_1$ relaxation')\n", "_=ax[1].legend(('Simulation',rf'$T_1$={T1:.0f} s'))" ] }, { "cell_type": "markdown", "id": "36aed0e8", "metadata": {}, "source": [ "The equilibrated magnetization is less than expected, because the 'recovery' option is not fully compensating the $T_2$ losses that are occuring for the nuclear populations." ] }, { "cell_type": "markdown", "id": "eac85f39", "metadata": {}, "source": [ "### Orientation-specific relaxation" ] }, { "cell_type": "markdown", "id": "f2a90946", "metadata": {}, "source": [ "The relaxation used above uses a single relaxation matrix that is applied to all spins in the powder average, regardless of their orientation or position in a rotor cycle. However, since the tilting of the quantization axis of the nucleus depends on the orientation of the hyperfine coupling, correcting the relaxation above requires application of a relaxation matrix that is orientation-specific. This requires use of the `OS=True` option (OS:Orientation-Specific). For $T_1$ relaxation, the `OS=True` option should be paired with the `Thermal=True` option if the system should relax to thermal equilibrium. The 'recovery' option should not be paired with these settings.\n", "\n", "Note, we may use $T_1$ and $T_2$ relaxation that is not orientation-specific, but paired with 'recovery' with `OS=True`. This is useful if the quantization axis is not tilted, but the polarization of a given spin varies with its orientation (e.g. an electron in the rotating frame will not tilt, but variation of the g-tensor may be large enough that the electron thermal equilibrium varies throughout the rotor period)." ] }, { "cell_type": "code", "execution_count": 22, "id": "da6b34c5", "metadata": {}, "outputs": [], "source": [ "L.clear_relax() #Remove existing relaxation settings\n", "L.add_relax('T1',i=0,T1=T1,OS=True,Thermal=True) \n", "_=L.add_relax('T2',i=0,T2=T2,OS=True)" ] }, { "cell_type": "code", "execution_count": 23, "id": "39227e54", "metadata": {}, "outputs": [], "source": [ "seq=L.Sequence(Dt=1e-3)\n", "rho=sl.Rho('1Hx',['1Hx','1Hz'])\n", "_=rho.DetProp(seq,n=15000)" ] }, { "cell_type": "code", "execution_count": 24, "id": "8685a87d", "metadata": {}, "outputs": [ { "data": { "image/png": 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fbi688MLAexpjjNfrNTfffLMZPHiwGTJkiHn11VeNMcZ88cUXZuLEiebss882AwcONBdeeKHxer0xXXOkzx1YZJrBfae5/jn66KNj+mwPNx6P12zYtd+8sXirufe/35mrXlxoch/6wmQMPdG0P+FK0+u290zPW9814ko1XY87y5z1r7nmqhcXmnZdephTr7zVvDhvs3l/+TZz/i+vMc+89rbZWlRq9pSUm7ffedds2bLF9x4es2vXLlNeXh7nq1XKEu1+mDgVQKxkd926dQwcOFA7j6tGdc+7q1mzfX+DnvPIbm24+7TBNR4zadIk7r33XgYMGMCJJ57Ieeedx8SJE0OOKS0tJTc3lz//+c+ceeaZ/P73v+eTTz5hzZo1XHrppUybNi3mmJ599lkyMzMpKytj9OjRnH322Tz44IM8/vjjLFu2rNrxb7zxBsuWLWP58uUUFhYyevRoJkywvqkvXbqU1atX061bN8aNG8fcuXM5/vjjY45FqXBllR4WbtnDJwvXsGjtJvKTulFS7mb7s9fjyuzGMVfex8DOrdmZVsXQvhn89sqxZLdPY80J79C/X1/69LH6iT15ydaQ857yzBMhj6eddmpg2+Fw0KlTp8a/OKUOUUIlgEu++pgrf38tX3/9tf5iUYeljIwMFi9ezNdff80XX3zBeeedx4MPPhhyTHJyMpMnTwZg6NChpKSk4HK5GDp0KFu2bKnT+z322GO8+eabAOTl5bFhwwY6dOgQ9fhvvvmGCy64AKfTSefOnZk4cSILFy6kTZs2jBkzhuxsq+P0iBEj2LJli/6cqjr7oeAA7y3ayPtfLmBLUg8q3V52v343zoN7uOFfb3NUj3Zs6HIbA3p25pyzcq0XXTIn5Bw9Jp3U5HEr1dQSKgE8YtQ4HnnkkQbpCK9UTWqr1DUmp9NJbm4uubm5DB06lBdeeCHkeZfLFaiAOxwOUlJSAttutxuApKQkvF5v4DWR5tqbM2cOn376KfPnzyc9PZ3c3Nxa5+SzWiMi88fhvwZ/LErVZmvRQf773QY+2bCftTv2WwMLVn7CnbPm8dMh2ThO+wet01M56qih1gtGXRPfgJVqBprdPIAi8qyI7BaRVVGezxWRYhFZ5vtzV6znTk5N56abbiIzM7PhAlaqGVm/fj0bNmwIPF62bBm9evWq83lycnJYtmyZNQ1BXh4LFiyodkxxcTHt27cnPT2ddevW8e233waec7lcVFVVVXvNhAkTeO211/B4PBQUFPDVV18xZsyYOsenlNvj5aPVO7nkme8YddUD/G7aaDx7t3HXqUfy7r/u5YtPP+buM4aTO7ATE8Ydy1G+TvpKKUtzrAA+DzwOvFjDMV8bY06t4fmI/LWHDz/8kAMHDnDOOefUIzylmq8DBw5www03sG/fPpKSkujXrx8zZ86s87/1cePG0bt3b4YOHcqQIUMYOXJktWMmT57MjBkzGDZsGAMHDmTs2LGB56666iqGDRvGyJEjefnllwP7zzzzTObPn8/w4cMREf7yl7/QpUsX1q1bV/+LVgmlvMrDv7/ZyIN/n8HBNj3IOWI41587iR877uGuXxxbry88SiUiqalJJl5EJAd4zxgzJMJzucDNdU0AU7r2N3+b9SHX5vblxBNPpLS0lPnz5zdIvEoBrF27liN8Q/lV04n0uYvIYmPMqDiF1GBE5FngVGB3DffDt4HNvl1vGGPure28o0aNMosWLWrASBtfpdvLS9/+yIwvf2Bn4V52PXUlp55zPq898y+SnM2uMUupZiPa/bA5VgBjcayILAe2YyWDqyMdJCJXAVcBJHfph9eX7D733HN07ty5qWJVSqn6ep5GahFpSb5Yt5tf/+VpfvjuY0698X7+fv5R9LzZGjGuMzooVT8t8WvTEqCXMWY48A/grWgHGmNmGmNG2TPfSreXC17ZwJcb99bYIV0ppeLNGPMVsCfeccTL7pJyrnxxEb94fiEVxYV08RTwxM8GcWzfDnTv3l2TP6UOQYtLAI0x+40xB3zbswGXiERfkyr0tRQeqCB/bxm3PPU+I0aM0GZgpVRLd6yILBeRD0Qk6vBzEblKRBaJyKKCgujrgzYX7y7fxsgLbmH2Bx8wfcoglr3yZ9avWq6D+JRqIC0uARSRLuL72iciY7CuoSiW19oLfsltO9GmTZtap61QSqlmrF4tIh07dmyq+Oqswu3h9jdWcP2/F7J/6WyO8a7lmol9SUtxkZTUUnstKdX8NLufJhGZBeQCWSKSD9wNuACMMTOAc4BrRcQNlAHnmxjbcg3BkcDOlDS+/vrrBo5eKaWajjFmv217toj8S0SyjDGF8YyrvnYUl3HxI2+xsSyda08YxKU3z6Nzp+abrCrVkjW7BNAYc0Etzz+O1Sm6Hueuvq+yspJVq1ZFnOZCKaWaMxHpAuwyxpi6tog0N+t3lnDeo++y4m+Xc+5lVzN9yunxDkmpw1qzSwAbkzdCBvjrX/+al19+mfz8fNq0aROHqJRSKrLGbBFpThZt2cMvn19IWrtO3HnPn/jVZRfGOySlDnsJlQDa74r+sWPXX38906ZNIyMjIx4hKaVUVI3ZItJczPuhkLNu+CM5w47l9RvPpEfmifEOSamE0OIGgRySCF+MBw8ezJQpU3A4EuujUIenp556ihEjRjBixAgcDkdg+6abbqrX+X75y1/SqVMnhgwJnYP4ww8/ZODAgfTr148HH3yw1v1KRbJk614u+9en7Pny3wwtnkePzPR4h6RUwkiorMcQeTF6t9vNI488wmuvvdb0QSnVgK688kqWLVvG+++/T48ePVi2bBnLli3j0Ucfrdf5LrvsMj788MOQfR6Ph+uuu44PPviANWvWMGvWLNasWRN1v1KRrN2xn8ueXUDXLp2Z9+0CnvjH3+MdklIJJbESwCg9Y5xOJ6+++iqffPJJ0wakVCNZtWoVQ4cOPeTzTJgwodq8awsWLKBfv3706dOH5ORkzj//fN5+++2o+8Nt2bKFQYMGccUVVzBkyBAuuugiPv30U8aNG0f//v1ZsGABAKWlpUydOpXhw4czZMgQ/YJ2GNldUs5Zd/yTkmUf8PIVxzBq6ECd4kWpJpZQCaDXmIgzx4sIn3/+OU8//XQcolKHq9zcXJ5//nkAqqqqyM3N5aWXXgLg4MGD5ObmBpKa4uJicnNzeeONNwAoLCwkNzeXd999F4CdO3fW6b1XrlxZrdk23Pjx4wNNxPY/n376aY2v27ZtGz169Ag8zs7OZtu2bVH3R7Jx40Z+/etfs2LFCtatW8crr7zCN998w8MPP8z9998PWM3J3bp1Y/ny5axatYrJkyfHevmqGSuv8nD1vxezbcEHpG78nM4ZrniHpFRCSpivXEL0JmCA1q1bA9Yv4jZt2ugSQ6pFW7VqFSeddFLg8VtvvcX777/P7t27ue6665g0aVK958GM9DMkIlH3R9K7d+9AhXLw4MGccMIJiAhDhw5ly5YtAAwdOpSbb76Z2267jVNPPZXx48fXK17VvNz19iqWbt3HKy+/wjHdU3C5NAFUKh4SJgGE0CbgSL+Yli5dSm5uLi+//DKnnnpYr62umsCcOXMC2y6XK+Rxenp6yOO2bduGPM7Kygp53KVLlzq998qVK/ntb38beHzGGWdwxhlnsHfvXm6++WYmTZrE+PHjKSkpqfbahx9+mBNPjD4SMzs7m7y8vMDj/Px8unXrFnV/JCkpKYFth8MReOxwOHC73QAMGDCAxYsXM3v2bG6//XYmTZrEXXfdFeMnoJqjN5fk89Q/H+N3N17LqSOy4x2OUgktsRJATNR+gABDhgzhwgsvpHfv3k0XlFINzOv1smHDBgYNGlTtuT/96U9cd911APWuAI4ePZoNGzawefNmunfvzquvvsorr7zCwIEDI+6vr+3bt5OZmcnFF19MRkZGoDldtUxbCku5ecY7FH/1ApnnjgJGxTskpRJaQiWAmOgDQcCq0jzxxBNNF49SjWDjxo1kZ2eHVNmMMUyfPp0pU6bUadWbCy64gDlz5lBYWEh2djb33HMPl19+OY8//jgnn3wyHo+HX/7ylwwePBgg6v76WLlyJbfccgsOh0N/Nls4t8fLr19bRkb3fnzy9bf8ZKyuvKRUvEkLnDS+XlK79Td3Pf0OFx3Tk4kPzaF7uzTmTv9pxGN37NjByy+/zO9+9zvtC6hitnbtWo444oh4hxHRY489xgsvvMDo0aMZMWIE11xzTbxDajCRPncRWWyM0RJTFKNGjTKLFi1qsvebOWcDf3zpU2bccDrThkfuFqCUahzR7ocJUwEUBK+35iZgv/fff5/p06dz8sknN8hUGkrF24033siNN94Y7zBUAtpadJC7/vJ3dn80gx7XjQU0AVSqOUioaWAMoesBe7yGaY9/w+frdoUcd+mll7J+/XpN/pRS6hAYY7jjzZW0H5LLH//0ACNGjIh3SEopn8RKAE3oesD7y6pYkV/MTf9ZHnKcy+Wib9++gDV/m1JKqbr7aPUuvtlYyPQzRnHX7bdolxqlmpHESgBrGQUc7o9//CNjx47F6/U2XlBKKXUYqnB7uO3xVyl58x5+0iNhehsp1WIk1E+lMaGT2NaWCx555JHs27eP8vJy0tN1kXJVOxNltRnVOBJlEFtL9OK8H9m+YwftHQfpmNUh3uEopcIkTAXQ/ys50q+LaL+uzz33XP72t79p8qdikpqaSlFRkSYlTcQYQ1FREampqfEORYXZd7CSxz7fwNQzzmbDmpWkpaXFOySlVJjEqQCKNQDEW49fzitXruTHH3/U1UFUjbKzs8nPz6egoCDeoSSM1NRUsrN1RYnm5snP17N77QJuu/pGrYgr1UwlTgKIvwm47q/77W9/S15eHqeccgoOR8IUTVUduVwuXUVGJbx9Byt57Knn2f3Oo+z7zYnQ9dh4h6SUiiCxEsCwQSCxNtU99dRTtG3bVpM/pZSqxdNfb8Y1YDx/fXIYY8eOjXc4SqkoEiYBFKzqn78JWAS8vvyvtiYKe1WnsrKS5OTkxgpTKaVarOKDVTw/bwtTj+rJby7U5d6Uas4SqqQVXu+rS2d9YwynnXYav/rVrxo2KKWUOky8NH8zm1+9lxHyY7xDUUrVImEqgFC9D2BdugOKCKNGjaJDB53OQCmlwlV5vDz94SKS9m+jrVMn0FequUuwBDB0FHBdRwTffffdDR2SUkodFmav3MFeZ1ve/Pw7cgd2jHc4SqlaJFYTcNhScIE+gHU8z+zZs3nvvfcaKiyllGrRjDHM+HgFOZmp5A7spAPmlGoBEqYCKIhvFLCtAuit+5wwXq+Xu+66i7Zt2+q8gEopBSzZupdvXnmMjL3f471pPQ5HwvxqUarFSpyfUvGPAj600zgcDt588006d+7cMHEppVQLN2tBHu2POJbrjz6RpKTE+bWiVEuWUD+pxvb/UPc+gH49evQAoKqqiuLiYrKysg49OKWUaoH2l1fx3ortXPSzM7n1rKHxDkcpFaOE6qhhrwDa5wGs37kM48eP5+KLL9a1X5VSCeudZdspWv4Fp/RvHe9QlFJ1kFgVQBO6Ekh9K4AAj3++kSk/+zmjBvXStS6VUgnrqXe+ovDdh1h6Yjbjh94Y73CUUjFqdhVAEXlWRHaLyKooz4uIPCYiG0VkhYjENN28YDX+2qt1h1K4e+ST73muoBdTp06t/0mUUqoFW7tjP1s87bn7mXf4+c9/Hu9wlFJ10OwSQOB5YHINz08B+vv+XAU8EeuJrXkAQx+D1RwcU2BzN7N2x/5q+2fOnMnvfve7WMNQSqnDwtvLtuNyOrjxvJNp165dvMNRStVBs0sAjTFfAXtqOOR04EVj+RZoJyJdYzo3YEIGgdQttj++u4Ypf/+62v7lq9exfMUKqqp09nulVGLweg3//u87pC2dhctbEe9wlFJ11OwSwBh0B/Jsj/N9+6oRkatEZJGILPJ4PFaTb8hScKEZ4NvLtrGjuKzWAMIHfbyXPJHWZ9yNy+WK8RKUUqplW7x1L9s3rWXbok9IS0uLdzhKqTpqiQlgpAbbiLU8Y8xMY8woY8yopCQnXlsTsCB4vcFjK9wefv3qMi6Y+W3ENw2ZQDrs3cSZxNK8Yvbu3cvrr79ep4tRSqmW6O1l2+h8/Lls/OEHnftPqRaoJSaA+UAP2+NsYHssL6zeBOzfDiaDO4rLI77WY8v6PFHaju+77z4uueQSduzYEUs4SinVIlV5vLy3fDsnHdmFzDat4h2OUqoeWmIC+A7wc99o4LFAsTEmtowrbCUQE6E5ONqAEHcMCeBdd93FvHnz6No1pi6JSinVIi3cvIeN//0LP7zxaLxDUUrVU7Or24vILCAXyBKRfOBuwAVgjJkBzAZOATYCB4FfxHru8LWAIw0IkYgtzKFzBnqizB/Tpk0bRo60ZqXJz88nOzs71tCUUqrF+HjNLlLaZDFiYE68Q1FK1VOzSwCNMRfU8rwBrqvfuUM7C9oLed5apoQJaQL22BLHCNXA9957j7POOovPP/+c448/vj6hKqVUs2SM4ZM1uzjjypu5/7LR8Q5HKVVPLbEJuN6MCZ37z570GW/k12wtOkhZpSdkwIinlmpgbm4uN954I8OGDWu44JVSqhlYt7OErdt3ctKRneMdilLqECRMAigIXttScPZkEIKJXHgBcMJDX3DFiwtx2zLAmgaE5O05iDcphYcffpg2bdrg9Xp1rWCl1GHjo5Xb2f70tXz5b+3/p1RLljAJIPiXgrM9jtgELLbnrX1zNxaFVv1qSADH/+ULTvvHNwDs27ePE044gWeffbahLkEplUAaa2nMQ/Hxqm0MPvWXnHf2GY39VkqpRpQ4CaBYCZ83pAk4+LQ3QpXOntz5C4Aioc2+7gh9AH8sOghYg0Latm1LSkpKQ1yBUirxPE8jLY1ZHzuKy1izu5xrfnUdubm5jflWSqlG1uwGgTQuEzYIJNjsG0jwbM/bkzt/E7AQOggk2pQwAA6HgzfffDOkqqiUUrEyxnwlIjk1HBJYGhP4VkTaiUjXmKfGqqNP1+6m/McVTOitgz+UaukSpwJI9X5/3kjbtlwtcgVQgv0FpeYE0H88wOzZs7n55psPJXyllApXr6UxCwoK6vVm781dzq5X7+DD11+s1+uVUs1HwiSAQvU+gPZyYKRELtJoX4ct6XOI1JoA+s2dO5fPPvuMkpKSuoaulFLR1GtpzI4dO9b5jSrcHpYXwYV3P8mFF15Y59crpZqXhEkAwaryRZsHMEIBMKyp19cEbEv6HELI6OCaRvvee++9zJs3j9atW9c7fqWUClPvpTHravGWvZR7nfzi3NPp1q1bY7yFUqoJJVQCGDIIhChNwDZur73qR+B1/gRQwiqANVUDnU4naWlpVFZW8oc//IGioqJDvBqllDqEpTHr6Kvvd1O65D26JR1ojNMrpZpYYiWARJ76BWzzANoGbHhN9aZeR1gF0BMyUKT25uB169bx0EMP8c4779T7OpRSicG3NOZ8YKCI5IvI5SJyjYhc4ztkNrAJa2nMp4BfNVYsH369gMJPZrB04beN9RZKqSaUUKOATVgTsAl7DkKXgnN7g/tCkr5AFTH2CqDfsGHDWL9+Pb169arfRSilEkZjLo1ZF/sOVvIjHfnDS59z2mlHN/bbKaWaQMJUAP2Jnb2fnokyJ6Cfvw9g6Mjf8D6Atm1P7QkgEEj+1q1bx6xZs+p+MUop1YS+3bQHY+DU44bTpk2beIejlGoACZMAgn8amODjkPV9/dU+2/H25eE8EauBoU3D9gEhAPl7D7K/vCpqPPfeey+33HILBw8erOcVKaVU4/tm3XaKP3sSKdoS71CUUg0koRJArzEh/f4iTgptawMOjvyNnPSF7HdUnxLm+D9/wZS/fR01nhkzZjB37lzS09Prf1FKKdXIPv9uKQdWfsbOHdviHYpSqoEkTAIoRKgA2kcBe6u/xh1D0ueO0Bxst21fWdSY2rRpE2gOfu6559i9e3edrkkppRrbntJKtju78Mh7i5kyZUq8w1FKNZCESQBBMGFLwRnbYA779DBfrNtNQUlFSNXP/rwnyujgWPsAhtuyZQvXXXcdjz32WL1er5RSjWXhlj0AHNevE0lJCTVuUKnDWgIlgGHzAIqEDPzw7/cawy+eX8gFT30b0i/QXg30RpgGJlIfwFjl5OQwf/587rnnnnq9XimlGsvCTQUU/O8e8lfMjXcoSqkGlFgJYOD/fI8jJID+RG/j7gOUVXoA3yhh2+TPbtt2tDkB62r48OE4nU727t3LPffcg8fjqfe5lFKqocxf9QNJZXupLI/enUUp1fIkVgJoQhuBQ1cCsf62N+PeMGspEJro2fsAWpVBq+rncAhVIUvH1S8ZfOedd7jvvvtYsmRJvV6vlFINpdLtZWNpCjfPeJtzzz033uEopRpQwiSAIv4m4OA+r30eQN8T9sRtd0lF4Hn7YA/7CiGRVgsRgSpP/ZqDL730UtauXcvo0aPr9XqllGooa3bsp8LtZWTP9vEORSnVwBImAYTqS8HZtz2BJuDqiVt4ohdp8mdrFLD1WqftmPro27cvAJ988gl33HFHyOTVSinVVBZv2cOOF3/Lyk//E+9QlFINLLESwLAm4JBt32akvM0R1uzrjdgHUEKmh6lyx14BNMawPcJ0MR999BHvv/8+paWlMZ9LKaUayncbttM6qzs53TrHOxSlVANLrASQYIJnJXLB52rusycho4cDFUBH6Ohgfx9ApwhVdRgR/PrifI578HOWbt1LSXkVj322gSqPl4ceeoivv/6ajIwMvF6vVgKVUk1q9e5Kzpv+COeff368Q1FKNbDESgDD2oDtc/t5a0iuQpp6HdimgbE3DQeTSGfYgJDarN2xH4BFW/by5JebePST73l9UT4iQps2bfB6vVx99dX85je/0SRQKdUkdu0vJ39vqfb/U+owlTAJoLUSiAlp4o3WH7Daa8W+LrCETAQdTAyD8wCKgLuWQSCLf9zDgDs/oKCkgi5tUgHYub+cVJf1nyRvb+j6wK1bt6Z169YhS9UppVRjWfLjXna9PJ33Hr8r3qEopRpBQk3rbhUAI/cBrKkJWAid/NkdYUoYezJoVQBDE8D/LMwjJ6sVY3pnAvDSt1up9Hj58vsCsjJSACsBHNilNQC7issB2F1STqfWqTzyyCOBc23dupVOnTqRmppa9w9BKaVisPjHvWT0O5rJPx0f71CUUo0gYSqA4FsL2PY40pQwkYQmfRLSBOwx1RNDpwiV7tDz3fq/FZz75PzA446traRvd0k5Dt9/hV3F5aS5nADsKC7nw1U7GXPfZ8z/oQgRQUQoLy/nJz/5CZdcckndPwCllIrRkq17mXjeNVx91ZXxDkUp1QgSJwEUq+IXSPok8kTQEV9qXws4bE5Ad5RRwPbm4Eg6+RPA/RWBwSillZ7A+xQcqOD7XSUAfLWhIPC61NRU/u///o9bb701xguH1duLte+gUipmFW4Py3/YwYjureMdilKqkSROAoivAuhPhKJMCh1JeFNvYBoYBI/H1u/PvyqIbSJoZ5QMsE2aC7ASPf97G2Ns09EYura1mnjDp4i58MILAxNFP/PMMyxcuDDk+bJKD7e8vpw9pZV8t6mIqY99w7Nzt0S9PqWUslu3o4RdHz/JE9dPi3coSqlGkjAJoCDVB3rYpnapuQlYQucBtB3rH+wb0gfQPiWMIzQBzJn+PkUHKgJt0QUlFaETUtuy0lYpVhfNSHMEApSXl/PAAw/w6KOPhuz/35J8Xl+czyMfrydvr/Xa1dusKuDL3/0YWONYKaUiWbNjP+kDj+O6G38T71CUUo2kXgmgiIwSkeSGDsZ2/skisl5ENorI9AjP54pIsYgs8/2JaZia15hg8iahFcAaB4GEVwBNcL+xNQ2HTATtqwAmOapXABdu2ROIo8rjDWuKrj4wxb8kXbjU1FTmzZvH008/DUBJSQlerzeQdLo9Bv/be41hzvoC7nxzFffNXhP1WpVSakX+ProOHccdv7sx3qEopRpJnRNAEekKzAMaZWVwEXEC/wSmAEcCF4jIkREO/doYM8L3595Yz2+iNPvWOA0MtmlgqvUdDG67Q+YB9Aa2w5PLvQerAkmk19YUbTVRV4/P4zV4vYZvNhRW68vXqVMnWrVqxYGySoYedyLnXXBhIAH0GGPbhrIqq/JXWFIZ/WKVUjFr7C/D8fLSl6sp2rUj3mEopRpRfSqAlwIvAFc0cCx+Y4CNxphNxphK4FXg9IY4sTGhK4FESwbDOSRC83Hgdf7zCZ5AH8BgE3CS01FtSpi9BysDU9AYW1XSGqQSYaJqgbeXb+PiZ77j9cX5EeN4fXE++zsPx9t9eKDq6PEaHL4+iF7btqembFcpFZPG/jIcLxVuD6WrvmDbE5exe/fueIejlGok9UkALwFuB5JFpG8DxwPQHcizPc737Qt3rIgsF5EPRGRwpBOJyFUiskhEFlVWVmAIrgVsLQsX4zyAEjp/oNcbOUmzzw9orwBWhiWA+2wVQPvAFGNsyZkB+8sqfWsLf/tDUdQg24w6ncETT8PpEMo2L2HNNx8GE0ATbA42xlDl8XL7GyvYURy5f6FSqlaN/WU4Lj5evYu0Pkcz+uLpdO6sawArdbiqUwIoIj8B1hljCoHngMsbIaZIw2bDs7MlQC9jzHDgH8BbkU5kjJlpjBlljBmVkpJSrYk19pVAJKS/oP3QSAM47ANCkhwSSN789h2sDCR9XhOcjtpKSoPH2Ucbt0u3Wpl+KDgQMUZ/1c/tNSQ5HJQsfpfF7zwHXnfgffzNwV4DX28oYNaCPH7/5qroF66UqkljfxmOi8/W7sLVIZtXH70z3qEopRpRXSuAlwPP+LZfA34mIg09kjgf6GF7nA1stx9gjNlvjDng254NuEQkq7YT21cCqT6at+aJoI2tYuetrRoIgapfpFVB9pRWBV7nNcFzWNPARI7Jf8x23woh4ZKcjsBxTofQ8cw7mXLz30lyuTDuKgq2bgw2AXsNQjBhVErVTRN9GY6LNxdvpXzrCtq7dLYApQ5nMSdvItIOGAt8AFYSBnwLnNLAMS0E+otIb1/n6vOBd8Ji6SK+RXFFZAzWdURpGw3y2ubZg9BK3l8/+T7q6wQJWTYutO9gcNuf59krgPl7y7jwqe9CzldW5Q5W/cLWJ661eTkstlW+6V2ctgqg0yGIM4mUNh1wiFA8/zXe+eOl7N6RHzivf3pCTf+Uqpem+DIcF1VFeeyadQcffjA73qEopRpRzGsBG2P2Af3C9jX4emTGGLeIXA98BDiBZ40xq0XkGt/zM4BzgGtFxA2UAeebWJa6MOFLwVmPSivd7DtYVcPLgkmawYT02Ys2aMNe9dtcWBpyviqPsY0Ctg8CidwEDMHmZfu80h+s3MG1Ly/hb+eNCBn44T+f22vF2vro0xg8oC9duvcAdlBRVhYyOEQpFTvbl+FLwPoyLCL+L8PvxTG0Q2aMIaldFzqdey8nnHBCvMNRSjWiQ/rG6puypcEZY2YbYwYYY/oaY+7z7ZvhS/4wxjxujBlsjBlujBlrjJkX03mJPPVLeB+96vEED7aPJPaGN9na1gsOb/a1W7B5D28t3RY4X+AUYQmlffJp+5JzfpuLrMRy7c79gQpglccbSOr8yaAzvS19jj8Nj9dL1d7tvHP7mcz7/KPANQDM3VhIhbv2Jp/SCjc509/n6a834fUabnptGcvz9tX6OqUOF8aYfcaYfvYvncaYS4wxLTr5A/h20x4cyWn0HHYsnTp1inc4SqlGdKhNFjNFJB1ARCY0QDyNxpr2JbQJ2J8o+efHi8ZembMGbVSv2BkTmrD5p4GJZuW24sD5ok4EHdK8HJxiZm9pJTfMWsreUms+P7fH4PL1AfR4TaDvoNtjAs3SxliPJSmFToOO5oghwwPnXbWtmIue/o4HZq+LfP3G8M8vNrKjuIyiA9Z7Pj9vC4WlFbyxdBtXvrioxmtV6nAnIi+KSJpvu12cw6m3C576loMbF7An74d4h6KUamSHmgDeBTwjIv8GRjdAPI3KPgjEgK0fXs2vK6v0BJKq8AqgP2ELb8qtqQIYEpPtfFFHAYuEDNZYsGUP7y7fzlNfbwbAbXsvt9cEElGP1wTWJ/Yaa39S6w6M+eW9tO/UBYDvnvs//vaXBwBYv7MkYoybCkt56KP1XPvSkkDyKwLekD6PXnKmv8+L87fEdN1KHWYcwBO+JPCmeAdTX8YYimb/jaH75sY7FKVUIzvUBPD/gPVYuct/Dj2cRuQbyRtss6l58me7bfvKeGKO9Y04ZCBJWPLmT7yMMSFJWU1CEsdq/QGrNwc7HNZaw3ZVYUlfsA9gcJk5Kxn0bRsrMTRej5XJ2ZaLixij73UHKtwhCao/yXUIlFZYVdSHPlof03UrdZjZDPwReAJoFd9QDk2Xnz/KI/fdHe8wlFKNLKYEUEQG+EfdhrnVGPNH4Fqg2d8x7MlbeLUtVvYqor0PoNeYkCphZS1NwMGYQieZDplX0DatjH9UsUOqTyzttq0nbFUAfa+3bYdUK73Gag52OBl5yZ1cfsPNABT8sJLTTjuNHTusJaDm/1BEua153BgT0l+ywrcttpicEdY+VupwUcO98CljzBasJHBykwbVgEQEV7su9O172ExrqJSKItYK4BvAPhFZKCLPishvROQEfLUjY0wpcHVjBdlQ7KN2wwdwxKr6xM3BjDIwnx8m9ibgkBHGoSuSRBwFTPVBK6HNvsFBINZ+fxNwMIn0muCgEq+xbvoApYXb2LRpE23btmVzYSnnz5zP799aFRKf/7oECQwacTgIbovg9Rpypr/PjC+1H5E67ES7F5YBGGO2GGMirkzU3O3aX0553ioOrP6iXvdGpVTLElMCaIwZAnQCfgWcBvQF7gBWishO3zHNetZQ/8TH9n5/9bnHeb3YJnEOT96sbbfHRF2xI+L5okwrE8ghbfMAbik6yG9eWxZyDmuwh/V8lSdYiQyvANqbif2JnNVcbe3PHn0yK1asIDU1jX2lFex+7U4+/M8LwWTW2Kt+tm0ksO2Q4KCaRz+OPreiUi1RLPfClupP76/lwMpP2TfnOSIXOZVSh5O6zANYASwUkQPGmBv8+0WkfaNE1ghMSBOwidrnrTb2kb+RBoFsKixlU9jcf7HEFJJQho0O9lfyIgnv6+exVwDtzb62xNWf9HmModLjCewvOljFmPs+4+yhmThSMnAmp1HhtvoLeqoqA9VHASqqgkmfv6lYRALb2hysDkeHw70wkneXb6fDyddx3uCMeIeilGoCMSeANiFZkzFmbwPF0uhCRgGb+vUBDJkGxlZFtE8DUxceEzqxdLBPYWhlsKYl22av3Mk63whet20QiMdrQpac84SNCAarAulP6rwGthYdBOCdNXvpeOYddOmcQZXHS+nar/j2q+fZMuaDwPvam339FUCnCAcrQxPA7fvKyGyVTKqrUaaNVCpeWuy9MBpxuvjjhbnxDkMp1QRiHQTyuIhcLiJHUX01shYjpP9e2OCLOp0jQpXOPggkkpSkyB+1xxtMRD1hyZvHVrGrLbncVFDqe53XVgH0hlT9QpqAbcmgf8CKMYaP1+wCgvMYigiVbi+udl3IHHQMmZ2zATiwfSP79pf4jglWAO3VQKdDMMZw3IOfc/0rS6PGXnSgIvCa/yzMY5VvjkSlmpvD5V4Yiad0L/vmzmJn/tZ4h6KUagKxDgJZARwF/A1oLSJrROR1EblHRM5rtOgakDURtL0CaGqsqkXjraFKV9OyamN6Z0Y5ny3pM/aJm23Nt3WI1eMNViI9HhOyKoj/HP5Jof3b/grgmu37mfnVpmrxVXm8pHQ/ggHn3IzbC8brYdVzd/LArb8CQiuADocE+gAmOYLVwE/X7ooa89F/+pRrX1qMMYZb/7eCU//xDQA509/njjdXxnTdSjWRFn8vjORAhZuqwjyKv3mFbdu2xTscpVQTiHUQyExjzPXGmInGmCxgEvAccBA4tTEDbDAStnIHhExxEqvQiZtD++zVVKWL1h/OmsIleA57chnoG+iNvXm52pQw9gqlbR5A/8AO+3akJNNrSxCt6W08iMPJ4Ivv5ozLrO5P3oqDPPyHm6natxOHrQnY4RAOVLgBcDlDr/+xzzaw+Me9lJRbazB/sb6Avbb1mP0xvfKdVY149pvNzN1YGNNnoFRjaep7oYhMFpH1IrJRRKZHeD5XRIpFZJnvz131eZ91O/aT2msYPW56nbFjxx564EqpZq8+fQAxxuQD+cDshg2ncdkHbRgD5VXBgRUOgXH9svh6Q81JRmizb+jKIjU1ASdFSQD3l7sD06WENAGb0CZgd4zzCpZVecLmAaw+9Ut483JNayEbY0LmHfQf27b3YHoM7A1rV7E/bx3fvPs6meeOxCFQsGcvxl1FkiOVknJ/Amh916hwe/B64dFPvudvn37PR7+ZEPh8dhaXB7Z37S8PieHe99YAsOXBqTF9Dko1hca8F/rWWv8ncJLvPRaKyDvGmDVhh35tjDmk5POSZxYA4HCl4nK5DuVUSqkWos4rgYjIbY0RSNMwIXP1lbuDFUCX00FWRkqtZwjvR2hPpGpqAo5lRKyVAPrPHd4HMLZ5BfP3lrF0q9UX3T4/oNcbWqG0NwfXNGfhDwWl7PNV5gyRJ4LuOHAUT85eRErX/jgcwgv/fJRtT14OnkpKK4IJoDGGgb//kEufs37ZOB3CTl+i1y7dxc79Zb7tZLbvs/anuZwU+dY89vu/99bw9jJtplLx1QT3wjHARmPMJmNMJfAqcHpDnDi82l9W5WHf3FmUrvmyIU6vlGoBak0AReQ/tj+vA1c0QVyNwhhsTaLBaUzA6scWS4/u0JHE9oQNairSxZIA2iuU9mqg1xDSPFob/0AOe6XPXlG0J31eYwKJXDR3v7M68LqKkAQwOBG0I9Va/cohwtCxP6H1qGkkp6RyoMLNvnmvUrL2G3rfbhVJFmzeA1iJ3g5f1a9tmoudxRUAtE93sX2flQxmtkpm656DvnNbiewz32zm168uixjrgQo3T3+9CbfHy+rtxeRMf59NBQfYWVzOz59dQEGJ9R71af5XiS0O98LuQJ7tcb5vX7hjRWS5iHwgIjFNQv19hHW/D679ip5VOgBEqUQRSxPwfmNM4EYnIk80YjyNRvBX0qzHVjITTAJEiGnyU683fDk560Glx8uGXdVvqmAlLrGc22NCp23xn7ugpIJ3lm+v9fXhquz9AT2ho4Dt2xUxJkNWH8Dq8wAKEjInYN/hY2i7OR2nQ9hXWsHBNV/hPbifzJxjACjPW0VK9yNon+5ir6+6l56cFKgWJic52HvQ2p+RkkSeLwHs1DqV7cVlITH9Z2EeGalJbCo4wDUT+/LcN5t55JPvSU9OCiR7sxZspX2rZL76voAZX/7AKUO7cPYT83nlimM4rl9WHT9VlcCa+l4Y6aYR/jVzCdDLGHNARE4B3gL6RzyZyFXAVQDJXfpVe77bFU/w35smHEq8SqkWJJYm4PvCHt/ZGIE0BYNtuTZjAgkHWHfaWOYtDp/82Z8M7jtYFZiLL5xDBEcsCaCtCdierNZm8uAuEfdXeYLTwNi33V5vYJqX/L1lPPb5xtjeCKhyB6eH8VcDqzzekDkBy22jgMvdhq6X/5N2E38OQGXBFna9Mp0DKz4m1eWkrKIS4/X4KpHW64wJribicAh7fElim7SkwHQ3yUkOdpeUc+v/VvCrl5fw8Mff89ay7WSkWt9plmzdS9e2qQCs3VFCp9bW9rqd+1m/01qlZdbCPPL2HGTo3R+xenv0qWdW5O/DGMO+g5VM+uuXrNu5n90l5eRMf595GwvxeA2PfryewgMVMX+OqkVq6nthPtDD9jgbCPkmaIzZb4w54NueDbhEJOK3Gt8AllHGmFH2/fvLg60LOR11EmilEkWtCaAxZjOAiKSLyHBjzB7/cyLSU0QiNUk0S/YJlYtKK1mydV/gOXuS1jbNxUlHdo54jtB5AEOXbotGpB7JpbfmPoV2yVHmGPQaOOhLcqs83kA/QrfX4I41uwzjXzXE4w0mbFUeb2BAjTEERwGL8MmaXYgIDpeVgLnadyfrjNtJ7z+WFfnF3P/kK+Q/fgl7t28OJJQer6Hcdw4BDvgGkiQ5HOTttaqBlW4vY+77LCS2f3/7Iz/6JrL+oeBAoI9noW2ewV37KwIjkr/fWcLcjYWUVLj526cb8HgNby/bRqXby6ptxRhj+HZTEdMen8tzc7fwzcZCvt91gEc//j4wV+ETX/7Ad5uLeOzzjfz+zVWUlFdx3AOfBZq51eEjDvfChUB/EektIsnA+cA79gNEpIv4mhdEZAzWPb2oLm/yx7dXc3DDtxR9+A/Ky8trf4FS6rBQl0EgVcAbItLKtu9poGvDhtR47HPuVSNWogY1J2z2qWTsS7fVRGKtABp7BbDmUcV2/hG2kbww/0fAmtg5UAH01G8ORGMbMVzp9toqgCaQ9FV5vBSXWRWFdTtL+HB16PKokuSi1cBxOFtZq2Y5W7Unrd8YHG27UuH2UrLkfZY+fxcHyqxfRJUeb2AqmZKKKp75enPU+Jbn7eP5eVusY8vdlNliOlhpncNrTGBkcpXHG/hvvmFXCV9+v5tfv7qMaY9/w6n/+IaXv9vKbl8z8nebi0j2fc6lle7Al4DSCnegmlpUWsHKbcVsLy7nLx+uo7TCzQmPzOHbTdF/H+ftORjojzl75Y5As/W8jYXs8zWDx/pFQDWZJrkXGmPcwPXAR8Ba4D/GmNUico2IXOM77BxglYgsBx4Dzjd1nOH+jaXbcO/bRdmWZaSmpjbkJSilmrGYE0BjTBXwJnAeWN94gY7GmEWNFFuDEpEal2tziAT66TlEog7a8Nrm6iPGCqDDlly2Tkli6rDIvyc8Xvs8gLFVAEWiTzFjV+XxBs5nrRBS9wpgaaUn0DRb5fEG+v1VebyB5vRNhaU88030JC1cSreBZJ3yGyq8QkWVB+OuoKq8jEpj/dPc+PGLfDxrJgB5e8piXmN54+4DrN6+H7CSyNKKYOXSnwAC7Cm1ktVd+yv45fPWP2V/U/7v31oVqPQVl1UFXnegwhMYlFNa4QkkapXu4Pt4jWH19v38UFDK/723BrfHyx/eWsX3u0q4f/Zafig4wN7SSsb/5Qvue38tu0vK+dXLS7hh1hKKD1Zx4dPfcd0rS6h0e+lzx2z+8dkGwFqv1d8nUsVHU94LjTGzjTEDjDF9jTH3+fbNMMbM8G0/bowZbIwZbowZa4yZV5/3aTP6dLKveSamvspKqcNDXaeBeRr4hW/751gToLYYByrcUQdT2Kt+QvRBG14T7IUdkgzWwN68bL1P9Jusfem2mpLL9GRrXV2nCA5f4KkuB/07Re7DE9IH0FPzvIIDOlvnSE5yMG14t8D+4rIqXvrWGiVYVuWhuMxKfHYUl/PaorzqJ8IaxGE/RzQFJRUUlVbSZsxZ9L74T5RVWsllwZbvWbBkaeC4PZ89Renar2o9HxD4b11S7g5UAA9WejhQYSVv5VUeFm7ZE7ieSPwro3y7aQ9fbSgArKqfP+krrXRTeMDarnB7A9PaeAzs8A1YKavyMPaBz/j3tz9y2j++YeZXmzjhkS8DlcGPV+9kvS/p3FJ4kO93W9trtu9n3U4riX3yq00UHajghllLufLFRRhjuOk/y/h8nTXi29631f9vcmvRwUD1dFPBAYp9SeuBCreOgj50LfpeqJRSdUoAjTHrAERkAHAB8O/GCKox1Pa91kr6fNs1JWn2yaSxVumojZUA+rYdgrOGYNyB6Vlqnlbm3FE9gufz/Vd0ijAqp33E470GXvatquH2mkCzZbj0ZCfjfCNjM1KSyGyVDFj9InMHdgwcV1Lu5tO1u6MH6JOc5Aisg5yVkcxpNSSD763YAViJmT9B6XjGdLJO/R1gLUFXvnkpVQVWs7bLCSlfPUbZlmU1xrDvYBWvLrAS1APl7kAlb3txOZ+vq/0a/N5eZiWUG3cf4NFPvgesQTRrd1hJWmmlm12+aW32l1UFpqrZVFAakiT6XfvykkAcq7ZZ50hPcQaSwVYpSSzL22d9Dq1TmO9LGLftLePl77byxpJt/PL5Rdzy+nL63DGba19azPB7Puam/yzn49U7mfCQVV1csHkPP33kS+55dzVrd+xnyN0f8eAH6yg8UMFFT3/Lc3M34/UaXl+Ux3Lf+1W4PVS4PWz2VVzdHi9frNttrSPt8fL+ih2BqrJ/IAwQWNnlcNeS74V2xhiMp4pdr/2BfuXr4x2OUqoJ1WclkGewvv2uMMbsbeB44iZ0pK5E7QNoHwRSW5Xu7JHZ/G9JfkhC6bBV7CJ5y5dk1NQEnOQIxprkEJz+czuiN12H81eWwKocXnZcb2Z8+QNpLmegT6HLKYEBE8lJDgZ0bs2c9QUxnd8vJclBiss6X7LTQbrLqlw6hKj9Jw9Wenh/5Y7AYxHr9eJw0u2Kf2G8VnKYXFHMzi3rkczBZGWkMKYTPPPH62n/k1+Q2mNIoBImIpT4KmFlVR5eXRi5WhnuzKO68+bSbaS6HNX6Tfr7PAL8d3E+YDVRP/6FNaJ6c4xN1X5//nAdYCWLv39rFWAll3e9vTpwvutfsSqhJRXuwDEAr/ve/4NVVn/LN5du482l1kTZsxZsJd83cGbeD0V0bWf18XpvxXY2FZYyd2MRS7fu48EP1lWbD7Jduot9B6sY1KU1Xdum8sX6AiYM6Mi4vh144IN1XDCmB7kDO3H1vxfzy3G9OXV4V8761zx+P/UITh7chRtmLeXmSQPpmZnOuyu2c/qIbmzYfYCubVPJ6dCK1xflMXVYN9KTnTz22QYuObYXHVql8M8vNnL+mB50bp3KqwvzmDykC5mtklm9vZgBnVvjcjqocHtISXLW6TNuBC3+XvjKgq14yw/grSjlp/3axTscpVQTqk8C+B/g78C9DRxL46olLwpN0oLbHVun0DurVWBUp9sbXDvXvi5wuFbJzkAzbWj/QgIJW02sEcuRy4vOsKqf02E9SHIISY7Yirr+/nEAbVJdgUQv1eUM9ClMTnIEksFkZ7CSF4sJAzry1fcFvgqgM3C+NN9n0jurFcf27RBoUo5VlzapnD6iG09+tYm2HTpz4VOzmfnVJtKSHTiqShBnEq3S0/EAFVtXUvjew3Q6526SO/fFU1aCt6KUpLadIzbxd26Twvmje/L3zzbQrW0qPdqnAZCVkcJZI7N5zNcPrzZZGckUHqikd1YrTh7chRlf/kCvDulMHtKFJ7/cRPd2aRzfL4vXFuWRnuwkKyMlMNl1XYzJyWTBlj2IBNeNjsS/vOHO/eX88wtr2cHCA5V89b2VzNuTWTv/CjDrdpYE+kV+9X1B4HWzFuQxy1dZfXbuZj7yDfj50/tr+dP7awG4+JnvAud76KPqFaY/vb+W5CQHJeVuXpi3hd4dW7Fq237+/tkGxve3lmZ87LMNTB7ShefnbWFM70xG57TnublbOHtkNg6BxVv3cvbIbJZu3YeBmLocNJCWeS+0ufPNVThbtafrzx/l9utOiXc4SqkmVOel4IwxB40xbY0xnzZGQI2l9pRLQpqA/dsuh9CpdegScf5KS4Xby6drd0U8m5X0+bfto4pjGxEM8NHqyOe2VwBDmoAdEtOAEL+zR2YDkOJyBCqHToeQ5K8AOhwh1cBYE8B+nTIY2r2NdW5bE7A9AXQ5HbRNs9Yc7dUhnRMGdYrp3OnJTlJ8VcS0ZCdpLiciQmqSk74DjqDLRX+m35HDueXkgUhyGqm9huNsbTVpH1z3NdufvALPfqvZt2LHBtI2f8X0SX0BaJ3qorVvHsFUl5M2vviSnQ46+JrCB3TO4O7TjqwWl//5/p0ymD7lCCs+l5O+HVsFrrevb4619GQnY/tmAtClbSp3TrWO75mZzv+dMaTauU88Ijgl0V/OGQZYq6WcfXR333unBPa3S3fxzwtHBo6/eGzPwPbwHu2qnXtUL6vLQKfWKVwz0fochnZvG7jGId3bcOvkgQD0yWpFTod0gEDXALtt+8pIcwWrcvafm85tgtvZvsQa4IiubQJN8qWVnkBTOIQmrv7R3Qs27+GfX/zAwUoP//72R16Y/yOrtu3nnnfX8M7y7by7fDtXvtg049Ja6r3Qz7/2tp8OAFEqsdSnAnhYuey4HJ6ft8UaqetLEwX7oI26JVV+DnuSJhJaXazH+eycjmAzcpJt2yGCs6YOhjZ9Oraiv2+wh0MkkOiJWEmv9SA4x6BDJLCdkuSocfk4rzGkJgWrn/4KYJLDEUgQHCK0SbUSrDSXk9OP6s5nNfTHO7ZPB+ZvKgrpU5jkcJCWnBSIOyMlKfD+7dOTSenan27n3c5JR3bm1YV5pPYeSebkG7hs0miGZbfjyuufZfeS92jzm6sBKJz/Bv96YyVm3E20SXPh3l+I52AxbdPbBRKedunJZLe3kiB/c2iS00GfrFb84vmFZLdPo0sbq5k1ySl0bZvmu17IbmdtG6BnppUYVnm8DOzcOvC5nj+6B+8s28a1uX0Z0q0t7Vsl4xDh2pcWc97oHozpncmt/13BiUd0ZtKRXbjtfysZ1KU1U4Z04db/rmB0TiaTBnembZqLqyb04bqf9KNnZjrDstsxtk8HdpeU0yo5iX1lVXRvl8bBSjfvLNvOlCFdcXutuSIvOqaXb3WVUi45thdd2qZSXuXl7JHd6dYujQ9X7eT4flm0b5XM9n1ldGydwtod+xncrS3lVR4e/2IjV47vgzGGm19fzp1Tj6BNqosr/72Y+84YQuc2qVzz0mLuOvVIcrJace+7a7hyQm9yOrRi5lebOPOo7uzcX07enoOM79+R/y3JZ3C3Ngzt3pZ731vDBWN60ierFde/spQrJ/Smf6fWXP/KEq4Y34e+HTO4862V/Bj1X5LyG/uANY/mvm9eoWrPNnhwapwjUko1pYROADu1TglUoUJGAduaaUUINLHWhX3qF7EPApFgxa6+kpyOsEEltupdjMml05bYOm3T3jgkWAEUCDQNA4FErlObFPL2hC7JZufxGtJ9yZjbawJN4V5jaBXY7w189hVuL5npVoLVKtnJB7+ewISHvgicL3dgRyb078j8TUW4nA5SfUmkCKS5gh+mfxUQj9cEVgEBePDsYZw1MptFP+7hLx924ZShXfmh4ADtJl7K+ZddQVqq9d4Zacl4UlIRETJbJfPavx5g59x5tPurNffu/sXvsnVLCsdd9giTjuzM9cd3ZUhOVxwOB26Pl8uP782V4/sE5kEc3K1t4BrTkpPI8lXEWiU76ZlpJZFje3egZ2Y6V0/sw1lHZeNyOnj9muOqfaYzfx5cvGH+7T+lfXoyqS4n71w/juz26bROdfHlLblktkrG5XSw7K6TAhWdqyb0DbzWvyKK/79DenIS548JVgnvnBqsbtqrkTedNCCwbR/I082X1A7Lbhc4722TBwWef+4XYwLbb183LrD9v2uD1/jIucMD2zeeYK1i1iMzndE5VpXUX5kEePTcEYHtWVeNDZ77+uMD22/+ahxyHSpG4nAizoT+VaBUQkqYn3qJ0AgcPtrXXknz53yxzrMXziESeE/7WsCOsPesi8mDu/Dh6p1WH0D7IBB7BTDGZDVkrkPbNYYnfYFJpoVA5S3dlcS/LhrJr3yjWMN5vIZWvqTPSgat7UqPlwz/ttsbaGItq/TQvpVvu8pDj8xgE+EZI7pxwZiebCywlm+r8nhJdQWrkunJ/qofgWSrrMrD+P5ZXHZcDgO7WNW1Mb0zGdM7kwtG96R9q2T2lVUhDieTxw4N9HXLPevnDO3eltv+t5J26S5OOvtiViUPIisjhWP7dkB2rSOpKolWKUnM/Pkoxo8fT3JyMp999hlJTgdJK9/mo6JuXHrppTz/i9F0SyqlcxsHF4zpwRXj+9C7QyuuHN+bC4/pRcfWKbx/4/H07ZiBwyHc7ms2joW/qgjBxAugV4fgvMTanKdi1fa48+IdglIqDhImAYzUCdDeTw8I2w42B8farBpybkdo1c/epOzf7tY2leQkB1uKah8AkNkqmSO7teHD1TtDmpFDmpcdwUSuS5vUwJx00eLzV/octmqgPeEVW9MwBJuDDSaQbNn95sT+/O3TDXhDKoBeWvmStCqPl4wU63WV7mAFsNztob2vAug11vs+cNZQBnVpzVE9rT5qnX3NqpMGd6FDqxTfsYYuvkqfy+mwKoW2Ztk/ThtcLcb2vqbcKUO68OavjmNEj3aBEbsXjOkZSNrPGNGd0TlDKW7Tj1smDyQrI4WiFXNC5n289tprSUoK/gi99dZbHHHEEVx66aXkDuxETk4OEyZM4MUXXwTgkksuITc3l95ZVpVtw4IvcA4axKBBVsXMGKOJm1JKqSaROAlgBPb5+Yyx9QG0NQc76l0BtCdpYc3LtlG2JxzROaaVM5y2hFLCBpI4HbZk1Xbuu087knveXRPlfIQ0AQeafUVwJQWbgJNtCaB92o30wGAOocpjyMpI5pjeHYANuG0VQLcn2ATs9phAM22lxxvoA1hWGUwA/S6wNUsC5GS1YvMDpwTWS75mYl9G9mzH+P5Z/OmMIfTrlEF6chIv/nIMsRCRQHLZp2MGW2z9nzbeNyXwefzZN7jC/jq/Cy+8MOS57777LiRB/POf/0yXLl0Cjzdt2sSQIVazqtfr5ZxzzuHWW2/l/vvvx+Px0K5dO+666y5uueUWqqqquOKKK7jooouYNGkSVVVVvP3224waNYqcnBy8Xi+VlZW6dJc6JJUFP1Lw1gNcfPN98Q5FKdXEDrE3WssRLYWz/0KPVrGLdW49O6sJOPgeIQM17P3tYjx36GAPQmKyb/vP5zWmxjWC7f3+7FU/h1ijf/37XUnBpmF/E7AxBJpe/UlhWrKTVinBvn7+0b5urwkMzrAqgNZ2RVVoH8A0W0IZjf9zTHI6mD5lEJMGd0FEuHhsL8b26RD1dXWVdAidNO3/ns477zwmTpwYeDx37lxuu+22wONly5Zx7bXXAlBZWcnVV1/N8OFWf7iSkhLmzJnDjz9awxkKCgr42c9+xkcffQRAfn4+aWlpPPvsswDk5eVx/PHH89lnVsf+nTt3Mn36dNassb4A7N27l3fffZeCgoLA+xUWFuJ2B5fFU4kpOasnU0f3i3cYSqkm1iwTQBGZLCLrRWSjiEyP8LyIyGO+51eIyMhI56mNwxHa7BtpuTYhmBwN6JzBLScPjO3c9rn/bO8TOjjEGikaiyRnaFJqP4c/kTOYQPJiTGj1zs8/jYfDEZzkOXTgh4TEZE8i/RM6GwiM5m2b5uJ3Jw3ghV+MsQ3wMIFmX7fHG2gOrvIEk8FKj5c2aaEF6CcvOZqPfjMhps+jpXM4HAwZMoQePawVXdLS0nj44YeZNGkSAJmZmfz4449ceeWVAHTs2JEVK1Zw1llnAdCqVSvuu+8+Ro8eDUBVVRUpKSmBJult27bx17/+lS1btgCwevVqpk2bxtKl1mTS8+bNo2PHjnzzzTcAfP7553Tt2pXFixcHnp80aRIbNlhzHy5btoybbrqJnTutKZC+//57nn76afbvt6ZtycvL49NPP6W83Op2sHfvXjZu3BhIMKuqqqiqqopp6UTVdJI79qLjmXfwk7FHxzsUpVQTa3YJoIg4gX8CU4AjgQtEJHzitSlAf9+fq4Anaj9xpF0SMjgkkFRhG6hhGwUsSMSkKhKHo4aKom16mFgHbSQ57CN/w0Yp27JYe0UxOWzePofArb4RmvYJpO19B62kNHi9LlvTcHIguTSBfpFeY7jhhP706ZgRSO48XhOoBoY2B3tDmoBbp4b2Izx5cBf6dIy8lnGic7lcDB06lI4dreX4OnTowB133MHQoUMB6NOnD5999lmg4nj00UdTUVHBlClTABgxYgQLFy7kmGOOCRz/2GOPMWCANbq3Y8eOnHbaaXToYFVSKysrOXDgAA7fv5GNGzfy1FNPUVJiTQg9d+5crrzySvbssSZInz17NieddFLg8UsvvUT//v3Zt28fAI899hjJycmB1//973+ne/fuVFRUADBjxgxGjRoVSBCfffZZpk2bFrj+l19+mauvvjrw+I033uDuu+8OPP7ggw/417/+dYifcuLqkJFS+0FKqcNKs0sAgTHARmPMJmNMJfAqcHrYMacDLxrLt0A7Eela00mj1dnsLbBiS9LsyZs9OYp1Dr+QpM/2PvaKXV1GGDujzCsohC4tZz93eBPwlCFdg/Pw2aaMsSqAtoEftnOE9AG0TfKblZFMq2Qn06cEp/xIs4/8TQ4mg5EqgMYEYz3Pt66xanj+f9MZGRmMGjWKtm3bAtCzZ09uuOEGunWzpnQZOnQoM2fOJCcnB4Dc3FzmzZtH377WFCznnHMOJSUl9O9vTdNy/vnnk5eXR3a2NZn4GWecwddff01WljXp9qRJk/j3v/9NmzbWhODjxo3jT3/6E+npVgW6X79+TJkyheRkq+9n69at6dq1ayDesrIy9u4Nrq62adMmvv3228Djb775hhdeeCHw+PXXX+eBBx5oqI8tYRS89SAFb94f7zCUUnHQHAeBdAfsi7XmA8fEcEx3YIf9IBG5CqtCSFb33rSiutAmYN8+gomeYE+qhFgHBDvFvhJIaPJmH2EccxNweAJoS9Lspwhdxi303E7blDHOkMRWQvoA2vvAuWxzAgb6AGL1/Vt97+SQ82ckJzGuXweuGN8n2ATsNWQkB6t+/gTQb9P9p4T8N1AtQ1paWiD5A+jcuTOdOwdXLBk4cCADBwa7S4wdO5axY4Pz9k2dOpWpU4MDby666CIuuuiiwOPrrruO664LTub3hz/8gT/84Q+Bx48++iiPPvpo4PGTTz5JVVVVA1xZYknuOgBM9EndlVKHr+aYAEZKB8I7DsVyDMaYmcBMgJxBQ6s/jwmdB1D8fenC+un5B1Z4Dc5YBwiIvaIYOg9gtCbbcJ3bpDCubxZvLN0WNgo4mPTZE1Rs28lORyC5HNq9LTv3l3P1xD7sKa0MHJfktCV9toEfoX0Aq/cHjNaNy+EQXr7C+iXvXy+5Q6vkQGXQ/74pSY7AhL+HuiqKUmA1kbtc1acmUjVre8xZ8Q5BKRUnzTEBzAfsbYLZwPZ6HBNCkOoZYrVjgiI1sXqNCUneajtXsNk3dAoXfw5pMDX2AfzpoE4M7taWN5ZuIznJEdK867BV7xwRmnKTkxxUuq0r7tI2lXdvsFZKmLPeWm7NagIOzgPo79MniG0UsG1KGNvglVg68rucDv5y9jDG9ulAcpKDQV1ac+X4PgCs/9OUWl+vlGpcxnix1kDXL2FKJaLm2AdwIdBfRHqLSDJwPvBO2DHvAD/3jQYeCxQbY3aEnyhElHucvepnr0ZF6rNnIOZl3ERCB5gE38eEvI+/wta1bWq1EcbJzmDS53I6bFXEYHOwsSWl1vH+dXKFCrfH2m8bDOLP3ZwSfeqXQH9AQvsA+qOOdRznuaN70NM36vjD30zg7KOza3mFUqqpVGxbT95ff0b51pXxDkUpFQfNLgE0xriB64GPgLXAf4wxq0XkGhG5xnfYbGATsBF4CvhVbeeNbRBIIAbbKFv7ZNGhTcbhMlsl86vcvoH3C+lTGNLX0J+8BZPLJKc1n52dy7bmb0qSI/A6ay1g27YtSUyybVe6rWbYFFsS5/Fa6ZvTYeuLGD4IJLAdOsl0TodWXDCmJzMvCa5Lq5RqmZxprckYfjJJ7TrXfrBS6rDTHJuAMcbMxkry7Ptm2LYN0CDLvYdOBG3vAxisgtn31zQpdOc2qYG58MJHDIs96ZNgk3KwfyGB6VL8UlzBqp9V3cO3LbZtR+B8riRHyCCQk47szJFd23D9T4OTvHp8JUCHSKAp177aiRDaH9DO4bCWaFNKtXyuDtlknnBlvMNQSsVJs0wAG0NtFUBrKTj7/uqJIabmBDBkkuewdww5n61J2Z9seY2ptgJFstMZeF1yki0ZtFUDXUnBwR7JtgEbyU4H7dKTmf3r8SHn7NTamu/ryG5t8Pqbgx32EcvVEz+IvE8p1XJ5qyqQpGTtA6hUgkqYBDBSBmjsw30JT/p8x4Rt+xPAduku9h0MnXbCEaXfn7WyiO0ctlj8yZu/adbOlRRsfnbZmn3t28m2FUJcTgdu33miLQN3VM/2/O/a4xjRox1zNxZa8SGBZFBEAv0EhWBiWNOyckqplmf363cjjiTumTEr3qEopeIgcRLAKCL3AbRV6YwJDgKx9Q1Mcji49NhevDD/x5Bz2QeP2M9trxw6bNmgf5CFO0ICmJLkDEynYo0Ctva7wgaHOCP0+wtfBcTu6F7tAavq6I/Vn/Q5JDjIQwQGdGrN1RP7cPExvSKcSSnVUmUMPRHEwVE928c7FKVUHCRMWSdaI0foUnDBkboSkhhWHylsjOEK37QmtgPDXlf9HBCsDHqNCfQZPFjprhabNZVLMKELbQ62jrEPFHE5HVT6EsZYKnbG1gQcSAYJ9g0U3/XePuUIemSm13o+pVTLkTH0RDKG/JRj+3aIdyhKqThImAQwWgoYOjrXvl19pK59AEekASFWBdA+ejg4gjZSNdBAIAEsr7ISt/m3/5S/njccgGN6Z1LpsZIx+3Qs4dPD+HI+kpPEVjGsvV/PuH5ZnHVUd/7v9CHBZl+Bjr5+guP6ZdV6DqVUC2QMnvIDAKS7nLUcrJQ6HCV8E7BESPrAnugZW/+9YHOwfQSvn70VV4gywtiYkGQwfGm0rm3TOPOobM48ypoz77O11sTNyUmOQJXOvjqHPelzOR30zrIWvBsZQ7NOcpKDR88bAQTX8b3k2F5kt0/n61t/Qrd2abWeQynV8ngry8j/+/l0vuABHI6ptb9AKXXYSZgEMNJAN2PCkzT7/uC2vRrocFSvDPpVVHlCBn6Ejiq2bwfP0Sql5m/fgSZgW/8+l9OB2xMc7GFv9j2ubxZf3JxLToe6NdlmZaSw5cHgLwJt8lXq8CVOF+1/cjmuDj1qP1gpdVhKmAQwmpAULuqI4GDClmSvAIb1syur8oRVFIOntSeawSZgU60CGK7SE1zNI9AcnBSa9AUrgNZ5/VVApZSKRJJctBlzZrzDUErFUQL1AaxOxJ7omYj9Ae19/ewrgdiTQb+DlaEVwNCl5YLb/sTR4wkOAommylbpq3JHSvpC9yulVG2Mx43X1wdQKZWYEiZjiDQkwt7UC9GaeoMjgsOTwfAm4PLKYAVQwqaCth/q73Rd7vbWmrS1TXMBkJWRHKj6JScFk75kp4QkiUopVRt38S52/eeueIehlIqjhM8YIk3+DKFTv4SMAvZ9Yt4IFcCyKk9gZQ+P10RdZi7d1++vvMpTa3xXju/Dg2cN5eyR2bZKX2jS99MjOgFw5lHdY7lkpVSCc7ZqT9tjz4t3GEqpOEqcPoBRZkUJmavPdpDTVvZzhIwIDm6HVwDdXkNaspUAVnq8IcmlraWZ9GTrYy+LIQFMTnJw/pieACHNvoE+gEkO+nbMCBnAoZRSNXGkpJPe/5h4h6GUiqOESQCjTgQdKUkjfCm46iN/vWEjiP3SfM27FW5P4BxeYwIrc7i9hla+KVf8c+9dM7EvvbNqH3Wb7RuZ27djBiXl1sTRXdum1vo6pZSyM1UVeKvKcbj0/qFUokqYBNCeAvbt2IofCkrD9obP1Vd93j57Mohtzj+7NF91r6LKS6ovGazymEBiWF7lIT1s4Mf0KYNiuoKfHZ1N76xWjOrVHq9vCpnThnWL6bVKKeVXVZRH+aYlpA88Lt6hKKXiJOH6AHZuk8KNJ/QPPI7UTGvCtu19AJOcwWlgwrVPd9kqgMEEsKLKE2j2La/yBCqAdSUijM7JRERwOoTTR3QPGWmslFKxSGrbheTug/jDqUfGOxSlVJwkTAXQn9AlORwhffeirQQSedsE+gb6E8BbTh7I6JxMHALZ7dMpPFABWImef3WNCrc30Dew3O0N7FdKqXhwpGWQlJHJ5cf3jncoSqk4SZgE0M4+2CPS6h8AvsG8IVPCeO3Tw/iOu+4n/ULOfaDC6ptX4fYGqoGVbi9prqTAdrJO16KUiiNTVRnvEJRScZYwmUi0OfmgeqXPvvyb194H0AQrgBFagAFIt1X37M3B9qpfpMEjSinVVKr27Yh3CEqpOEuYBNAu0vq/1n5s+6tPCWPvDxiNP+kDQqaESddmX6VUM5HUplO8Q1BKxVniJICRpngxJmTC52jr/4q9MlhbAmhL9FJdkbfBGjAydVjXOl+GUipxiMhkEVkvIhtFZHqE50VEHvM9v0JERsZyXkdKWsMHq5RqURKmD2Ck6V6sbaptm7B1ge3Lv4Wv/hEuJSmYU9urgeEVwKV3TYoxcqVUIhIRJ/BP4CQgH1goIu8YY9bYDpsC9Pf9OQZ4wvd3jYzH3fABK6ValMSpANpSwGhNvRKx6hdlHsBo72J73l4N1HV6lVJ1NAbYaIzZZIypBF4FTg875nTgRWP5FmgnIrU2LXgrShs+WqVUi5JwWYlIWBIXeTPyusCm9j6AfoO6tCY1Sfv9KaXqrTuQZ3uc79tX12MAEJGrRGSRiCxypLRq0ECVUi1PQjYB12Xuv/CBH84YRvAuuOMEWqUk6STNSqlDEekGEj7/QCzHWDuNmQnMBEjp2j/KPAZKqUSRMAkg0Zp9bYcE5v7DvuZv6DQwjhhqpp3aRF5f86yR3TmqR7vYY1ZKJbJ8oIftcTawvR7HKKVUNYmTANrE1gew+jGxTAMTyeBubQB49NwRdX6tUiphLQT6i0hvYBtwPnBh2DHvANeLyKtYgz+KjTE6yZ9SqlYJkwBGGwUcpTtgxEmh69IH0G/ZXSdVmwJGKaVqY4xxi8j1wEeAE3jWGLNaRK7xPT8DmA2cAmwEDgK/iFe8SqmWJWESwEijgI1925ha+wB6bSuBxKpdenK9I1ZKJTZjzGysJM++b4Zt2wDX1efcY/tkHlpwSqkWLWFGAfvTtvBRwBJhKTiw9/sjZBqY+jQBK6VUczM6RxNApRJZwiSA0QaBRFsKTuzJoC0D1HV8lVKHA72TKZXYmlUTsIhkAq8BOcAW4FxjzN4Ix20BSgAP4DbGjKrb+4ScK+L+4Oof9uZgnTlBKaWUUi1fc6sATgc+M8b0Bz7zPY7mJ8aYEbEmf9EmeXZEqAxWa/a17VdKKaWUaumaWwJ4OvCCb/sF4IzGeJNoVT/7wA/7UnD2QSN+547KbozQlFKqaWh3FqUSWrNqAgY6++ewMsbsEJFOUY4zwMciYoAnfTPcVyMiVwFXAXTv0StwsY6Q+f6iJYPB7WBzsJUCbn7gFO0LqJRq0c4ZqV9ilUpkTZ4AisinQJcIT91Zh9OMM8Zs9yWIn4jIOmPMV+EH2Zc+GjZipNnv2x8y8MN2fMTm4LBt3zXUIVSllGp+slqHTlFVVVVFfn4+5eXlcYro8Jaamkp2djYulyveoSgFxCEBNMacGO05EdklIl191b+uwO4o59ju+3u3iLwJjAGqJYBR3yfC1C/hzb4h/QH9S8RpH0Cl1GFCwsYB5+fn07p1a3JycvRLbgMzxlBUVER+fj69e/eOdzhKAc2vD+A7wKW+7UuBt8MPEJFWItLavw1MAlbV5U1CRwEHt0OqfoGkL3SCaKWUOhyVl5fToUMHTf4agYjQoUMHra6qZqW5JYAPAieJyAbgJN9jRKSbiPhnw+8MfCMiy4EFwPvGmA/r8iaRVvyAKEvBQZ1X/1BKqeYu0m1Nk7/Go5+tam6a1SAQY0wRcEKE/dux1rvEGLMJGH4o7xOo7oXN6xcxMTRoBVAppZRSh5XmVgFsdOL7n58jwijg8HkAHQn3KSmlVNO77777GDx4MMOGDWPEiBF89913XHHFFaxZs6ZBzp+Tk0NhYWGNx9x///0hj4877rgGeW+lmptmVQFsTElOK6P7xbicQHInSNT+gBKlmVgppQ4Hze22Nn/+fN577z2WLFlCSkoKhYWFVFZW8vTTTzdpHPfffz933HFH4PG8efOa9P2VaioJU9tyiLDlwan8Ylzv4GhfTNT+gIEKoDGBeQCVUupwkexsXrf/HTt2kJWVRUpKCgBZWVl069aN3NxcFi1aBEBGRga33XYbRx99NCeeeCILFiwgNzeXPn368M477wDw/PPPc/311wfOe+qppzJnzpxq73fGGWdw9NFHM3jwYGbOtKaSnT59OmVlZYwYMYKLLroo8J5g/S645ZZbGDJkCEOHDuW1114DYM6cOeTm5nLOOecwaNAgLrroosCcsUo1ZwlTAbSLtBRcyJq/9mlgaH7flJVS6lDVNCjhnndXs2b7/qjP18eR3dpw92mDoz4/adIk7r33XgYMGMCJJ57Ieeedx8SJE0OOKS0tJTc3lz//+c+ceeaZ/P73v+eTTz5hzZo1XHrppUybNi3meJ599lkyMzMpKytj9OjRnH322Tz44IM8/vjjLFu2rNrxb7zxBsuWLWP58uUUFhYyevRoJkyYAMDSpUtZvXo13bp1Y9y4ccydO5fjjz8+5liUiofm9RWwiUTq92ftt/422Ff/0CZgpZRqbBkZGSxevJiZM2fSsWNHzjvvPJ5//vmQY5KTk5k8eTIAQ4cOZeLEibhcLoYOHcqWLVvq9H6PPfYYw4cPZ+zYseTl5bFhw4Yaj//mm2+44IILcDqddO7cmYkTJ7Jw4UIAxowZQ3Z2Ng6HgxEjRtQ5FqXiISErgNH6+kXqD2gwOg2MUiqh1FSpa0xOp5Pc3Fxyc3MZOnQoL7zwQsjzLpcrcM92OByB5mKHw4Hb7QYgKSkJr9cbeE2kuffmzJnDp59+yvz580lPTyc3N7fWOfpqatb1x+G/Bn8sSjVnWgG07Y808MNaL7ipIlNKqcS0fv36kCrcsmXL6NWrV53Pk5OTw7Jly/B6veTl5bFgwYJqxxQXF9O+fXvS09NZt24d3377beA5l8tFVVVVtddMmDCB1157DY/HQ0FBAV999RVjxoypc3xKNRcJXQGM1u/PPveffYk4pZRSjePAgQPccMMN7Nu3j6SkJPr168fMmTM555xz6nSecePG0bt3b4YOHcqQIUMYOXJktWMmT57MjBkzGDZsGAMHDmTs2LGB56666iqGDRvGyJEjefnllwP7zzzzTObPn8/w4cMREf7yl7/QpUsX1q1bV/+LViqOJFFGK40aNcr4R5Jt31fGcQ9+TqfWKbx+zbFMfGgObVKTePeG45n40BxapyTx2e8mMub+z0hOcvD9n6aQM/19Ul0O1v3flDhfiVKqNiKy2BgzKt5xNFcpXfubih2hfd7Wrl3LEUccEaeIEoN+xioeot0PE7oCCOHNwfb+gLYRIcDDPxvOyJ7tmiA6pZRSSqnGlZgJIJGbdCXCKGCvr0J6ztHZTRGaUkoppVSjS8hBICEVQNukgA6HvT+gtS8xGsiVUkoplUgSMgG0k2jbOvBDKaWUUoephE4ADeHLv0VeCk4ppZRS6nCS0AkgRF8JxD4NjFJKKaXU4UQTQFvSF20iaKWUUkqpw0lCJoCh/f6irAuckJ+MUkoppRJBQqY5/tG+bdNcOCLMCWhfIUQppVTTeOqppxgxYgQjRozA4XAEtm+66aZ6ne+Xv/wlnTp1YsiQIQ0cqVItX0LOA5iVkcI90wZz4pGdw5p9rb8NRhNApZRqYldeeSVXXnkl27Zt47jjjmPZsmWHdL7LLruM66+/np///OcNE6BSh5GErAACXHpcDt3bpYVUACMlg0oppZrWqlWrGDp06CGfZ8KECWRmZkZ9vrS0lKlTpzJ8+HCGDBnCa6+9dsjvqVRLkbAJoF+0PoD+ZPAoXf5NKXWYSXM5az0mNzeX559/HoCqqipyc3N56aWXADh48CC5ubmBhKm4uJjc3FzeeOMNAAoLC8nNzeXdd98FYOfOnXWKb+XKlbU2244fPz7QRGz/8+mnn8b8Ph9++CHdunVj+fLlrFq1ismTJ9cpTqVasoRsAg4RpQ8gwPs3Hk+PzPQ4BKWUUo0nqZk3caxatYqTTjop8HjTpk3cd999FBcX89///heAr7/++pDfZ+jQodx8883cdtttnHrqqYwfP/6Qz6lUS6EJoE348m+Du7WNWyxKKRVPc+bMCWy7XK6Qx+np6SGP27ZtG/I4Kysr5HGXLl3q9N4rV67kt7/9beBxnz59eOaZZzjnnHMC+8aPH09JSUm11z788MOceOKJMb3PgAEDWLx4MbNnz+b2229n0qRJ3HXXXXWKVamWShNAPxPaHKyUUqrpeb1eNmzYwKBBg2o8riEqgNu3byczM5OLL76YjIyMQJO3UolAE0AbHfirlFLxtXHjRrKzs0lJSTnkc11wwQXMmTOHwsJCsrOzueeee7j88ssDz69cuZJbbrkFh8OBy+XiiSeeOOT3VKql0AQwEl39Qyml4mLAgAGsWbMmZF9RURF33nknS5cu5YEHHuD222+P6VyzZs2q8fmTTz6Zk08+ud6xKtWSJXwCmJ5sjYa7JrdvoAKY6kr4wdFKqcOYtLDmjg4dOjBjxox4h6HUYSXhE0CX08GWB6cGHt8+ZRAnHNEpjhEppVTj6t4+Ld4hKKXiLOETwHBXT+wb7xCUUglORDKB14AcYAtwrjFmb4TjtgAlgAdwG2NGxXL+5j4NjFKq8Wlbp1JKNT/Tgc+MMf2Bz3yPo/mJMWZErMmfUkpBM0sAReRnIrJaRLwiEvVmJiKTRWS9iGwUkZpujEop1RKdDrzg234BOKMp3tQYHQHXWPSzVc1Ns0oAgVXAWcBX0Q4QESfwT2AKcCRwgYgc2TThKaVUk+hsjNkB4Ps7WsdkA3wsIotF5KqaTigiV4nIIhFZVFBQUO351NRUioqKNFFpBMYYioqKSE1NjXcoSgU0qz6Axpi1UOsItTHARmPMJt+xr2J9W15T04uUUqo5EZFPgUhLZNxZh9OMM8ZsF5FOwCciss4YE/ELtDFmJjATYNSoUdWyvOzsbPLz84mUHKpDl5qaSnZ2drzDUCqgWSWAMeoO5Nke5wPHRDrQ9434KoCePXs2fmRKKRUjY0zU9cpEZJeIdDXG7BCRrsDuKOfY7vt7t4i8ifUFOWoLSk1cLhe9e/euz0uVUi1QkzcBi8inIrIqwp/TYz1FhH0R2yyMMTONMaOMMaM6duxY/6CVUqppvQNc6tu+FHg7/AARaSUirf3bwCSsbjRKKVWrJq8A1vStN0b5QA/b42xg+yGeUymlmpMHgf+IyOXAVuBnACLSDXjaGHMK0Bl409dlJgl4xRjzYZziVUq1MC2xCXgh0F9EegPbgPOBC+MbklJKNRxjTBFwQoT924FTfNubgOFNHJpS6jAhzWnEl4icCfwD6AjsA5YZY04O+9aLiJwC/A1wAs8aY+6L4dwFQClQ2DjRN6ks9Dqam8PlWg6X6xhojGkd7yCaKxEpAdbHOYzm8m+tOcTRHGIAjaO5xQANE0cvY0y1fnDNKgFsbCKy6HCYLFWvo/k5XK5FryMxNIfPpznE0FziaA4xaBzNL4bGjqO5zQOolFJKKaUamSaASimllFIJJtESwJnxDqCB6HU0P4fLteh1JIbm8Pk0hxigecTRHGIAjcOuOcQAjRhHQvUBVEoppZRSiVcBVEoppZRKeJoAKqWUUkolmIRIAEVksoisF5GNIjI93vHURkSeFZHdIrLKti9TRD4RkQ2+v9vbnrvdd23rReTk+EQdSkR6iMgXIrJWRFaLyK99+1vUdQCISKqILBCR5b5ruce3v8VdC4CIOEVkqYi853vc4q5DRLaIyEoRWSYii3z7Wtx1NLXmcC+Mdm+IUywhPwtxiqGdiPxXRNb5PpNj4xDDb33/LVaJyCwRSW2i963T77omjuMh33+TFSLypoi0i0cctuduFhEjIlkN9obGmMP6D9Zk0T8AfYBkYDlwZLzjqiXmCcBIYJVt31+A6b7t6cCffdtH+q4pBejtu1ZnM7iGrsBI33Zr4HtfrC3qOnyxCZDh23YB3wFjW+K1+OK7CXgFeK8l/tvyxbYFyArb1+Kuo4k/s2ZxL4x2b4jTZxLysxCnGF4ArvBtJwPtmvj9uwObgTTf4/8AlzXRe8f8uy4OcUwCknzbf45XHL79PYCPgB/D73uH8icRKoBjgI3GmE3GmErgVeD0OMdUI2PMV8CesN2nY90o8P19hm3/q8aYCmPMZmAj1jXHlTFmhzFmiW+7BFiLdaNpUdcBYCwHfA9dvj+GFngtIpINTAWetu1ucdcRxeFyHY2lWdwLa7g3NKkoPwtNHUMbrF/6zwAYYyqNMfviEEoSkCYiSUA6sL0p3rSOv+uaNA5jzMfGGLfv4bdAdjzi8PkrcCvW750GkwgJYHcgz/Y4nzjcbBpAZ2PMDrBuoEAn3/5mf30ikgMchVU5a5HX4WsqWgbsBj4xxrTUa/kb1o3Ea9vXEq/DAB+LyGIRucq3ryVeR1Nqdp9D2L2hqf2N6j8LTa0PUAA852uKflpEWjVlAMaYbcDDwFZgB1BsjPm4KWMIE+3nOJ5+CXwQjzcWkWnANmPM8oY+dyIkgBJh3+E0902zvj4RyQD+B/zGGLO/pkMj7Gs212GM8RhjRmB9CxwjIkNqOLxZXouInArsNsYsjvUlEfbF/Tp8xhljRgJTgOtEZEINxzbn62hKzepzqMO9oTHeu64/C40lCavJ7wljzFFY69U3ad9MXx+707G6R3QDWonIxU0ZQ3MmIncCbuDlOLx3OnAncFdjnD8REsB8rPZzv2yaqLzdwHaJSFcA39+7ffub7fWJiAvrBv+yMeYN3+4Wdx12vuaZOcBkWt61jAOmicgWrOa/n4rIS7S868AYs933927gTazmzRZ3HU2s2XwOUe4NTSnaz0JTywfyfS0KAP/FSgib0onAZmNMgTGmCngDOK6JY7CL9nPc5ETkUuBU4CLj64zXxPpiJebLff9Ws4ElItKlIU6eCAngQqC/iPQWkWTgfOCdOMdUH+8Al/q2LwXetu0/X0RSRKQ30B9YEIf4QoiIYPVrWWuMedT2VIu6DgAR6egfASYiaVg3zHW0sGsxxtxujMk2xuRg/Rx8boy5mBZ2HSLSSkRa+7exOmuvooVdRxw0i3thDfeGJlPDz0JTx7ETyBORgb5dJwBrmjiMrcBYEUn3/bc5AatfZrxE+zluUiIyGbgNmGaMORiPGIwxK40xnYwxOb5/q/lYA6h2NtQbHPZ/gFOwRpr9ANwZ73hiiHcWVl+MKt9/8MuBDsBnwAbf35m24+/0Xdt6YEq84/fFdDxW89IKYJnvzykt7Tp8cQ0DlvquZRVwl29/i7sWW3y5BEcBt6jrwOo3tdz3Z7X/Z7qlXUecPru43wuj3Rvi+JkEfhbi9P4jgEW+z+MtoH0cYrgH60vtKuDfQEoTvW+dftc1cRwbsfrM+v+NzohHHGHPb6EBRwHrUnBKKaWUUgkmEZqAlVJKKaWUjSaASimllFIJRhNApZRSSqkEowmgUkoppVSC0QRQKaWUUirBaAKoWgQRaSciv6rlmCdFZFxTxaSUUs2B3h9VfWgCqFqKdkCNNzjgGKxFu5VSKpG0Q++Pqo40AVQtxYNAXxFZJiIPhT8pIkcA3xtjPGH7nxeRJ0TkCxHZJCITReRZEVkrIs/7jnH6jlslIitF5LdNckVKKdUw6nt//JnvvrdcRL5qqmBV85AU7wCUitF0YIgxZkSU56cAH0Z5rj3wU2Aa8C7WOqBXAAtFZATgBLobY4aA1ZzSYFErpVTjq+/98S7gZGPMNr3vJR6tAKrDxclETwDfNdaSNyuBXcZaX9GLtYxYDrAJ6CMi//Ct/7i/KQJWSqkmEu3+OBd4XkSuxPoirBKIJoCqxRORdKCdMWZ7lEMqfH97bdv+x0nGmL3AcGAOcB3wdCOFqpRSTaqm+6Mx5hrg90APYJmIdGjq+FT8aBOwailKgNZRnvsJ8EV9TywiWUClMeZ/IvID8Hx9z6WUUnFQr/ujiPQ1xnwHfCcip2ElgkWNE6JqbrQCqFoEY0wRMNfXYTm8k3NN/f9i0R2YIyLLsJK/2w/hXEop1aQO4f74kG/g2yrgK2B5Y8apmhexukYp1XKJyBLgGGNMVbxjUUqp5kTvjyoaTQCVUkoppRKMNgErpZRSSiUYTQCVUkoppRKMJoBKKaWUUglGE0CllFJKqQSjCaBSSimlVILRBFAppZRSKsH8P4/Vtxdfq2AuAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax=plt.subplots(1,2,figsize=[9,4])\n", "rho.downmix()\n", "rho.plot(det_num=0,ax=ax[0],axis='ms')\n", "ax[0].plot(rho.t_axis*1e3,np.exp(-rho.t_axis/T2)*ex.Peq[0],color='black',linestyle=':')\n", "ax[0].set_xlim([-1,500])\n", "ax[0].set_title(r'$T_2$ relaxation')\n", "ax[0].legend(('Simulation',rf'$T_2$={T2*1e3:.0f} ms'))\n", "rho.plot(det_num=1,axis='s',ax=ax[1])\n", "ax[1].plot(rho.t_axis,(1-np.exp(-rho.t_axis/T1))*ex.Peq[0],color='black',linestyle=':')\n", "ax[1].set_xlim([0,rho.t_axis[-1]])\n", "ax[1].set_title(r'$T_1$ relaxation')\n", "ax[1].legend(('Simulation',rf'$T_1$={T1:.0f} s'))\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "b06bb6e8", "metadata": {}, "source": [ "The desired relaxation rates are recovered. Note that some $\\langle ^1H_x\\rangle$ will remain even at infinite time. This is due to the nuclear quantization axis lying partly in the *xy*-plane, so the magnetization aligns there at thermal equilibrium. Similarly, some oscillation is observed at the beginning of the $T_1$ curve, which is the result of coherences oscillating in the *z*-direction. These are not errors, but simply what happens with a tilted quantization axis (however, the spectrometer cannot *see* static magnetization, so the constant part of the x-signal would not actually show up in an experiment). \n", "\n", "Orientation-specific relaxation is particularly important for calculating the [pseudo-contact shift](../Chapter5/Ch5_PseudoContactShift.ipynb), although should also be used for DNP experiments where the nucleus is titled by the electron, especially to correct polarization leakage as observed above.\n", "\n", "Note that orientation-specific relaxation is spin-specific, and so may yield unexpected behaviors when two spins are coupled in a triplet configuration, since the relaxation in this case is no longer independent." ] }, { "cell_type": "markdown", "id": "8fa5966e", "metadata": {}, "source": [ "## Thermalizing relaxation due to dynamics" ] }, { "cell_type": "markdown", "id": "f0787b2a", "metadata": {}, "source": [ "For some calculations, we want to see how a dynamic process induces relaxation, and in other simulations, we may want to see how relaxation affects some process or how polarization is transferred. In the former case, we do not introduce any relaxation directly, but instead add an exchange process, in which case magnetization can only be destroyed. In the latter case, we may introduce recovery of the magnetization, especially in case we are interested in polarization transfer. \n", "\n", "Occasionally, we would like to see how specific dynamics processes result in polarization transfer. This is especially the case for [Overhauser](../Chapter4/Ch4_OverhauserEffect.ipynb) and [Nuclear Overhauser](../Chapter2/Ch2_T1_NOE.ipynb) effects. But, it is sometimes impractical to do this if polarization is only being destroyed. Therefore, we would like to thermalize these systems as well. We can do this by adding a correction term to the Liouville matrix, which is added with by running `L.add_relax('DynamicThermal')`. Here we consider a simple two-spin system undergoing exchange to induce $T_1$ relaxation." ] }, { "cell_type": "markdown", "id": "96bdabc0", "metadata": {}, "source": [ "### Build the system" ] }, { "cell_type": "code", "execution_count": 16, "id": "2986526a", "metadata": {}, "outputs": [], "source": [ "# Lab frame for T1 relaxation\n", "ex0=sl.ExpSys(500,Nucs=['15N','1H'],vr=0,LF=True,pwdavg='alpha0beta45')\n", "ex0.set_inter('dipole',i0=0,i1=1,delta=22000)\n", "ex1=ex0.copy()\n", "ex1.set_inter('dipole',i0=0,i1=1,delta=22000,euler=[0,30*np.pi/180,0])\n", "\n", "L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(tc=1e-9))" ] }, { "cell_type": "markdown", "id": "cb935363", "metadata": {}, "source": [ "### Propagate and plot" ] }, { "cell_type": "code", "execution_count": 69, "id": "c2a6e40f", "metadata": {}, "outputs": [], "source": [ "seq=L.Sequence(Dt=0.1)\n", "rho=sl.Rho('15Nz+1Hz',['15Nz','1Hz'])\n", "_=rho.DetProp(seq,n=1000)" ] }, { "cell_type": "code", "execution_count": 70, "id": "f18dcd7b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho.plot(axis='s')" ] }, { "cell_type": "markdown", "id": "a67dc172", "metadata": {}, "source": [ "The dynamic process destroys the polarization on both spins." ] }, { "cell_type": "markdown", "id": "3111a6e0", "metadata": {}, "source": [ "### With 'DynamicThermal' option" ] }, { "cell_type": "code", "execution_count": 71, "id": "54575aff", "metadata": {}, "outputs": [], "source": [ "_=L.add_relax('DynamicThermal')" ] }, { "cell_type": "code", "execution_count": 72, "id": "2acb64ee", "metadata": {}, "outputs": [], "source": [ "seq=L.Sequence(Dt=0.1)\n", "rho=sl.Rho('zero',['15Nz','1Hz']) #Start without any magnetization\n", "_=rho.DetProp(seq,n=1000)" ] }, { "cell_type": "code", "execution_count": 73, "id": "c2702a07", "metadata": {}, "outputs": [ { "data": { "image/png": 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gnCMvL4+cnBw6duxY4/10iybUCjbDzEeh6/nQY5Tf1YiEpeLiYtLS0hTuR2FmpKWl1fovHAV8qH1wL1SWw4jfgX54RY5K4X5sJ/LfRwEfSl99BCve8nqJTK35n1UiInVBAR8qZcXw7t2Q1hUG3eF3NSLSCCngQ2XuX2HnOhj5e4iO87saEfmO1q5dy4033sill14KwMyZMxk8eDC33norM2fO9Le4o1DAh8LubfDZn6D7hRqhSSRCdOrUiWefffbAvJmRlJREcXExGRkHu/seP348ZsbKlSsPLOvZsyfr16+vz3IBBXxozHgYykvg/N/4XYmIfEelpaXs3bv3iOWDBw/mvffe4/HHH+fBBw92PbJkyRL69+/PO++8A0BJSQnbtm2jQ4cO1X7+zp07Q1M4Cvi69+0S+M9LXmdiaZ39rkZETtDKlSu566676N69O2vWrDlifVSUF5/NmzenpKTkwPKlS5dyzz33HAj45cuX07Nnz6O2gsnOzubqq6/mk08+wTlXp+dQq4A3s5+aWYsabptpZjPMbKWZLTezO0+sxAbEOfjgPkhoDkN+7nc1IlJLe/fu5fnnn+ess87ipptuomfPnixZsoQBAwaQl5fHrbfeypdffsmjjz7K1KlTueWWW7j22mu5/fbbD3zGihUrGD16NNu3b6egoIClS5fSt2/fox5zzZo1XH311Tz55JP06tWLRx55hC1bttTJ+dT4SVYzOwl4LLjPH2qwSzlwl3PuP2bWFFhoZh8651acWKkNwOp3Yf1nMPIPXsiLSK39+u3lrNhSWKef2attMg9e1Pu427Vp04aTTjqJZ555hh49ehyyLi0tjb/97W+HLBs79tDR2DZt2kRaWhoJCQkMGzaMDz74gCVLlnDSSScd9ZiBQIBRo0YxatQocnNzuffee2nfvj2zZ89m4MCBtTjLI9XmCv5G4H+A62qysXPuW+fcf4LvdwMrgXa1rrChqCiDDx+AFt29DsVEpMGZMmUK7dq145JLLuGhhx5iw4YNtdp/yZIlB67WR44cyTvvvHPcK3iAgoICJkyYwOjRo1mzZg3PPvvsMX8p1FSNruDNLA4YCfQBzjGzs5xz/67pQcwsCxgAfHEiRTYIi16GvK/hylcgoC5+RE5UTa60Q+X888/n/PPPJy8vj8mTJzNmzBhatGjBM888Q1ZW1nH3rxrmQ4YM4dZbb6WoqOjAsg0bNjBx4kTWrVuHmTF58mTGjRvHnDlzuOyyy3jxxRfp2rVrnZ1PTa/gvw984JwrAZ7Hu5qvETNLAt4AfuqcO+LvLjO72cwWmNmC3Nzcmn5seCnbBzMfh4yB0H2E39WIyHeUlpbGnXfeyaJFi3jkkUcIBAI12q9qwMfFxdG3b19iY2Np1qwZAB06dODGG28kEAgwfvx4AC6//HJWr17NY489VqfhDmA1+dbWzD4G7nbOfWlmAWAN0M85t+c4+8UA0/F+OfzpeMfJzs52CxYsqFnl4WT2k/CvX8D106HjYL+rEWlwVq5cSc+ePf0uI+TWr1/Pgw8+yFNPPUWTJrUf9Ke6/05mttA5l13d9se9gjezZsAW59yXAM65CuBJ4Jh3/81rE/QssLIm4d5gFRfCZ3+ETucq3EXkmEaOHElqaiqPPvoo+fn5IT/ecW8WO+d2Adcetux/a/DZZwb3W2pmi4LL7nPOvVvLGsPbnL/CvnwY+oDflYhImFuxon4bEdb0S9Z44DbgLMAB/waeds4dtXPi4Jewkd3/594dMOdJ6Dka2p3sdzUiIoeoaXOPF4HdwP8F568CXgIuC0VRDcbnT0BZEXzvfr8rERE5Qk0Dvrtzrl+V+RlmtjgUBTUYe/Ng/nPQ51JI7+53NSIiR6hpM8kvzez0/TNmdhrweWhKaiDm/tW7ej/7br8rERGpVk2v4E8DrjOzjcH59sBKM1sKOOfcd3/kqiEpyocvJkCvMbp6F5GwVdOAHx7SKhqaL8ZD6W44Wx2KiUj4qmnAdwJ647WgWeGcmxG6ksJccSF88TT0GAWt+/hdjYjIUR0z4M2sHTAVKAYW4jV7vNzMHgcucc5tDn2JYWbeBCgu0L13EQl7x7uCfxKvvfukqgvN7DrgKWBMiOoKT6V7vQebup4PbQf4XY2IyDEdrxVNr8PDHcA59yLQ48jNI9yXk72nVgfr6l2ksTl80O2G4HgBX20XamYWdbR1Eaui3HtqNfN0aH+a39WISD07fNDt/caPH89tt912yLLevXuzatWq+irtqI4X8G+b2UQzO9DtWfD934DI6lPmeFZOg10bYdBP/K5EROrR0Qbd3m//kH77FRcXs3Hjxmq7/g3lANvVOV7A/w9QAGwws4VmtgBYDxQCjec+hXMw+y+Q2hm6j/S7GhGpB8cbdHu/pUuXcvLJJx8y361bt2r7kA/lANvVOWbAO+fKnHN3A5nADcAPgQ7Oubudc6Uhry5cbPgctnwJg26HqFqNUy4iDUhtBt3eb/ny5YwdO5asrCyysrIYMWLEUYfoC+UA29U5bjt4M0sEujrnFldZ1h6oaDTNJD//CyS2gH5X+V2JSOR77x7YurRuP7N1Xxjx2HE3q+2g25s2bSI9Pf2Q++233347nTp1qvbzQznAdnVqcjlaBkyteh8eeAZoU+fVhKPtq+CrD2DgzRCT4Hc1IhJCtR10e8mSJfTufegYsitWrDjmINuhGmC7OjUZ8KPMzN4ErgCeC169pzvnGuDYeidg7lMQHQ+n3uR3JSKNQw2utEOltoNuL126lF69eh2ybPny5Zx00kn1PsB2dWp6Q/kZ4AfB99fhDbwd+YryYcnrcNLl0CTN72pEpJ7UdNDtwwM+Pz8f5xytWrWq9wG2q1Ojvmicc6vMDDPrhjfYx1mhLStMfDkZyvfBwFv8rkREfHKse+Mvv/zyIfOpqals374d8AbY/tWvfsXTTz99YIDt0aNHh67QatSmScizeFfyS5xz9duY0w+VFTB/InQ4U52KiUit1fcA29WpaW+SAK8DfwYeClEt4WXNB96DTcN+43clItIA1fcA29WpccA754qAlBDWEl7mTYDkdl63wCIiDZCe2qlO7hpYOwOyfwCB2vyRIyISPhTw1Zk3AQKxcPINflciInLCFPCHK9kDi1+F3mMhKd3vakQajfrom6UhO5H/Pgr4wy2f6o23mv1DvysRaTTi4+PJy8tTyB+Fc468vDzi4+NrtZ9uMB9u4QuQ3gMy675fCBGpXkZGBjk5OeTm5vpdStiKj48nIyOjVvso4KvauhQ2L4Dhj4GZ39WINBoxMTF07NjR7zIijm7RVLXwBQjEwUlX+F2JiMh3poDfr7TI63em1xhITPW7GhGR70wBv9+Kf0JJAZxyg9+ViIjUCQX8fgtfgLSu0GGQ35WIiNQJBTx4g3psmgunXK8vV0UkYijgARb/HaKi4aQr/a5ERKTOKOArK7wvV7sM05OrIhJRFPBrZ8Dub6G/BtQWkciigF/0CsQ3g27D/a5ERKROhSzgzew5M9tuZstCdYzvrLgAVk2HPt+H6Di/qxERqVOhvIKfBIT3ZfHyf0J5MfS/2u9KRETqXMgC3jk3C/BnIMKaWvyK1/a93Sl+VyIiUud8vwdvZjeb2QIzW1CvPcnlr4WNc7wvV9X2XUQikO8B75yb4JzLds5lp6fXYzPFxa8BprbvIhKxfA94XzgHS/8BWWdBSju/qxERCYnGGfDfLoL8b6DvpX5XIiISMqFsJvkKMAfobmY5ZnZjqI5Va8ve8Lom6Dna70pEREImZCM6OefC89HQykpYNhU6D1W/7yIS0RrfLZpNc6Fws27PiEjEa3wBv+wNiE6A7iP9rkREJKQaV8BXlHtPr3YfDnFJflcjIhJSjSvg182Eoh3QR7dnRCTyNa6AXzYV4pKhy3l+VyIiEnKNJ+DLS2DldOgxCmLi/a5GRCTkGk/Ar5sFJQXQ+2K/KxERqReNJ+BXvOXdnul0jt+ViIjUi8YR8BXlsOod6HaBBvYQkUajcQT8hs9hX766JhCRRqVxBPzKaRCTqNYzItKoRH7AV1Z6rWe6nAexiX5XIyJSbyI/4HPmwZ6t0GuM35WIiNSryA/4FdMgEAtdz/e7EhGRehXZAe8crHwbOp0L8cl+VyMiUq8iO+C/XQQFG6GXWs+ISOMT2QG/+j2wKOg2wu9KRETqXYQH/LuQeRo0SfO7EhGRehe5AV+QA1uXQnddvYtI4xS5Ab/mfW+q2zMi0khFbsCvfg9SO0OLrn5XIiLii8gM+JI9XvfA3UeAmd/ViIj4IjID/ptPoKJU999FpFGLzIBf8z7EN4PM0/2uRETEN5EX8JUVXsB3PR8C0X5XIyLim8gL+JwFUJQH3Yf7XYmIiK8iL+DXvAdR0er7XUQavcgL+K8+hPZnQHyK35WIiPgqsgK+8FvYtkxX7yIiRFrAf/2RN+06zN86RETCQOQFfNM20LKX35WIiPgucgK+ohzWzoAuQ/X0qogIkRTwmxdAcQF00e0ZERGIpID/+iOwAHQ6x+9KRETCQuQE/FcfQsapkNDM70pERMJCZAT8nlxv/NWuah4pIrJfSAPezIab2Woz+9rM7gnZgb752Juq/buIyAEhC3gzCwB/BUYAvYCrzCwk7Rf3rfwA1yQdWvcLxceLiDRIobyCHwh87Zxb65wrBV4FxtT1QQqLiilZ9SGfu35s2lVc1x8vItJghTLg2wGbqsznBJcdwsxuNrMFZrYgNze31gdpEg2revyEiXvO5Pz/ncUzn62lvKLyxKsWEYkQoQz46p42ckcscG6Ccy7bOZednp5e64MEYuM5/cr/x6P//SMGdU7j4XdWcsETs/hoxTacO+JwIiKNRigDPgfIrDKfAWwJ1cHaNkvgmeuzmXhdNs7BTS8u4KqJc5m/Pj9UhxQRCWsWqqtcM4sG1gBDgc3AfOBq59zyo+2TnZ3tFixY8J2PXVZRySvzNvLnj74ib28pA7NSue3czgzplo6pGwMRiSBmttA5l13tulDexjCzkcATQAB4zjn322NtX1cBv9++0gpenb+RibPWsqWgmO6tmnLN6e25eEA7kuNj6uw4IiJ+8S3ga6uuA36/0vJK3lq0mZfmbmBJTgEJMQFG92vL2JPbcWpWKlFRuqoXkYap0Qd8VUtydvH3Lzby1qIt7CuroFVyHBf2bcuofm3on9FMYS8iDYoCvhp7S8r5eNV23l68hU9X51JaUUmLpDjO6Z7OOd3TGdw1nZQE3cYRkfCmgD+Ogn1lfLJqGzNW5fLpmlwK9pURiDL6tkthYMdUBmalkp3VnGaJsfVem4jIsSjga6G8opLFObuYuTqXuWvzWLypgNLgg1PdWzWlf2Yz+mSk0LddCj1aNyU+JuBrvSLSuB0r4KPru5hwFx2I4pQOqZzSIRWA4rIKFm/axbx1+cxbn88HK7by2gLvAd1AlNG1ZRK926bQpWUSXVsm0aVlEpmpiQR0L19EfKaAP474mACndUrjtE5pADjnyNm5j+VbCli6uYBlmwv57Ktc3vhPzoF9YqOj6NSiCZ1bJtEhNZHM1EQymyeSmZpA22YJxAQio5dmEQlvCvhaMjMvsFMTGd6nzYHlBfvK+CZ3D19v28PXuXv4evselm0u4INlWymvPHgbLMqgTUqCF/YpCbRKiadV0zhaJcfTMjmeVslxtGwaT2y0fgmIyHejgK8jKQkxnNy+OSe3b37I8vKKSrYWFrMxv4ic/H1s2lnEpvwiNu3cxxfr8tlWWHzIL4D90prEkt40jrSkWJonxpLWJJbmTQ5OU/e/Er15/VUgIodTwIdYdCCKjOaJZDRPhM5Hrq+sdOwsKmVrYTHbC0vYVljMtsIStu0uZnthMfl7S9m8s4D8vaUUFpcf9TiJsQGaxkeTHB/jTRNiaBofQ3J8tDdNiD4wnxwfQ2JsgCZx0STEBkiMDZAYG01ibEC/KEQiiALeZ1FRRlpSHGlJcfRue+xtyyoq2VlUys69ZeTvLfVeRaXs3FtK4b4ydheXU1jsTXfuLWVDXhG7i8so3Fd+oCXQ8cQE7EDY7w/+hNgATaq8j4uOIi46QFxM1MH30VHB+f3ro4iLqfL+sO1jA1FEB4zogBETFaUHzERCQAHfgMQEomjZNJ6WTeNrvW9xWcWB8C/cV0ZRaUXwVX7wfUk5RWUV7CutYO9h7/P2lrJp5z72lVZQUl5BSVklJeWVNf7FcTyBKCM6yogJRBETMKIDUcREBacBb3l0wIiOiqryy8HbZv+6mEAUgSgjYEZUlBGIguioKKLMex8VXBeIMqLMO563XZV9zKslEBXl7RPcfv8+gSrbB4L7G952UQaY997wjuf93vKmFtwmKtjhXZQZZgf3teA2Bz/PgssO3dcIbld1XwyL4oh997PgNvvfe1XtX2dV3h9cJg1fWAX86tWrmTRpEjfccANlZWUMGzaMm266iXHjxlFUVMTIkSP50Y9+xBVXXEFBQQFjxozhjjvuYOzYsezYsYNLL72Uu+66i4suuoitW7dy5ZVXcs899zB8+HA2bdrEtddey/333895553H2rVr+eEPf8ivf/1rhgwZwurVq7nlllt45JFHGDRoEMuWLeP222/n97//PaeeeiqLFi3ipz/9KU888QT9+/dn/vz5/PznP+fJJ5+kT58+zJ49m/vuu4/x48fTvXt3Pv30Ux588EGee+45OnXqxEcffcTDDz/MSy+9RGZmJu+//z6PPfYYr776Kq1bt+btt9/mj3/8I1OmTKFFixZMnTqVv/zlL7z11lukpKTw2muv8fTTT/Puu++SmJjI5MmTeeaZZ/jwww+JiYlh0qRJTJo0iZkzZwIwceJEXnvtNT766CMAnps4nrfffpv33nsPgD//+c98/PHHTJs2DYA//OEPzJkzhzfeeAOAxx57jE2LFvHqq68C8Jvf/IbVq1czefJkAB544AE2bdnEs88+R2lFJffdey+5O/J45E//R0l5BQ8/cB9FRfv46YOPUVJeyZ8f/gUVlY5rf/YgJWUVPP/7XxKIiePiW++htLySV//3fhKSUvjetT+jrKKSt/7yC6JTW3PypbdSVuH4119/QdPWHeh94Q8or3B8Nv5+mrbrQseh11Be4fjyuftp0r4Xbc66jArnWP3iL0nqNIC00y6motKx/uX7SewykOSTL6TCOba+8gsSewymaf/hAGz9+z0k9T2PpL7n4SrK2fba/ST1u4Ck3udSWVbM9n/8iqYDRtKk59lUluxl+xu/IfmU0SR2H0RFUQG5/3yU5IGXkNjlNCr27CR32uOknH4ZCZ1Oobwwlx3T/0jKoCtJyOpP2a6t5L37BM3Ouob49n0py8sh74MnaXb29cRn9KQ0dz35H/6N5uf+kLg23Sjdtpb8jyeQOvRmYlt1ouTbNeyc8Rypw24lNj2L4pyV7Jr1AmkX3E5MWgbFG5ey698vkzbyp8Q0a82+9YsomP0qLUbdRXRyOvvWLqRg7j9IH/3/CCQ1p+jrLyic9ybpF99LIDGFotWzKVw4jZbf/yVRcU0oWjWLwv+8S+vLf0UgNoHdyz5h9+J/0fbKh4mKjqZwyYfsXvIxGdc+DkDBl++zZ8UsMsc9gmHsXDCdPV99Qfurf4MBeV/8k6L1i+hw5a8B2DFnCkU5K+lw+S8xM7Z/9hrF276hw2X3YcC2T1+meEcOHS/1hnX+9pMXKC3IJWvszzGDnH89S0VRIVkX/wwz2PjeBCrLSug05g4A1k9/CoCsUbcBsO6tvxAVE0fWyFsA+ObNPxGTmEKH4TcB8NWU3xGXkk77YT8AYM1rj5DQIpPModd686/8hiZtu5BxzlUArHrpVzTt0IuMIZcDsGLS/aR0GUC7s76PYSx79h5Se51B2zO8Ae2WTryb9H7n0Oa0UQAs/tvP6DToQv7z0m9PKPeOJawCXhqeqCgjPipAXEyAhNgAmamJALRIimNfoJJBnVsA8FZaEwAuz/aGCJjbJpmEhAR+fG4XAFb+oxlpaWk8cJE3bG/OW6lkZrbioSsHADDuvTS6d2/HL288DYArP2lB//5Z3HPHYAC+/+90zjijC3ffPRSA0XP/wtCh3bnzzvMBGDHvCS66qDe33TYSgPPm/y+XXtKHG344nErnuGD277hqdB+uHDeM4pJSLp37R64c1YtLLjuXPXv2csPcZlw1sifDxwxm165d/GRuClcM7865w89gZ14e/29eCldd0J0zv3c6O3K38sD8ZMZd0J1TBw9k65YcHlmQzDXnd+PkM7LZvHEDf1jYlHHDutE3+2Q2rUvm/xY1ZdywrvTo15/1X8UzcXES1w7tSqdeJ7FudYBJS5K4bmgX2nftzdfLK3hlaROuPbcL7Tp1Z82SfUxZ3oRrz+lMq8xOrF5UwLQViYw7uyMt2rZn5YIdvL8qkeuHdKZZemtWzNvKh6sTuWFIJ5qmprO0SQ4zvvLmk1JSWRy3js/WJvKDIZ1JSEziy6g1zF6XwI2DOxMbn8DC8mXMWx/PTYM7EoiOYX5xSxZuiOeHZ3bE4Zi/O40lm+O57ows7986rzmrcuO5emB7AGZvbc7aXQlclp2Jw/H5phRy9iQw9uQMAD77pinbShIY3a8tzsFnq5qSV57AiL6tcQ4+XZpEoe1hWK9WAMxcmMi+2DK+16MlzsGMuQmUlRqDu3o/e2XNvL94B3dtgXNQnBJPdGw8Z3bx1u9JjiehaQJndPaaQhc0jaNp80RODzaNzk+KIzXVm3c4djSJJb15AgM7es/KbGsSQ5vmiWQHn53ZkhhDZvMmDAjOb0yIpn1qIv06eA0w1sdH0755In0ymwHwTVw07Zon1P5/vhrQk6wiIg3YsZ5kVZMJEZEIpYAXEYlQCngRkQilgBcRiVAKeBGRCKWAFxGJUAp4EZEIpYAXEYlQYfWgk5nlAhtOcPcWwLGf2408OufGQecc+b7L+XZwzqVXtyKsAv67MLMFR3uaK1LpnBsHnXPkC9X56haNiEiEUsCLiESoSAr4CX4X4AOdc+Ogc458ITnfiLkHLyIih4qkK3gREalCAS8iEqEafMCb2XAzW21mX5vZPX7XEwpmlmlmM8xspZktN7M7g8tTzexDM/sqOG3ud611zcwCZvalmU0Pzkf0OZtZMzObYmargv/eZzSCc/5Z8Od6mZm9YmbxkXbOZvacmW03s2VVlh31HM3s3mCmrTazC070uA064M0sAPwVGAH0Aq4ys17+VhUS5cBdzrmewOnAj4PneQ/wsXOuK/BxcD7S3AmsrDIf6ef8Z+B951wPoB/euUfsOZtZO+AOINs51wcIAFcSeec8CRh+2LJqzzH4//aVQO/gPk8Fs67WGnTAAwOBr51za51zpcCrwBifa6pzzrlvnXP/Cb7fjfc/fTu8c30huNkLwMW+FBgiZpYBXAg8U2VxxJ6zmSUDZwPPAjjnSp1zu4jgcw6KBhLMLBpIBLYQYefsnJsF5B+2+GjnOAZ41TlX4pxbB3yNl3W11tADvh2wqcp8TnBZxDKzLGAA8AXQyjn3LXi/BICWPpYWCk8A/wNUVlkWyefcCcgFng/elnrGzJoQwefsnNsM/AHYCHwLFDjn/kUEn3MVRzvHOsu1hh7wVs2yiG33aWZJwBvAT51zhX7XE0pmNgrY7pxb6Hct9SgaOBl42jk3ANhLw781cUzB+85jgI5AW6CJmY3ztyrf1VmuNfSAzwEyq8xn4P15F3HMLAYv3F92zk0NLt5mZm2C69sA2/2qLwTOBEab2Xq8W2/fM7PJRPY55wA5zrkvgvNT8AI/ks/5PGCdcy7XOVcGTAUGEdnnvN/RzrHOcq2hB/x8oKuZdTSzWLwvJqb5XFOdMzPDuy+70jn3pyqrpgHXB99fD7xV37WFinPuXudchnMuC+/f9RPn3Dgi+5y3ApvMrHtw0VBgBRF8zni3Zk43s8Tgz/lQvO+YIvmc9zvaOU4DrjSzODPrCHQF5p3QEZxzDfoFjATWAN8Av/C7nhCd41l4f6ItARYFXyOBNLxv378KTlP9rjVE538OMD34PqLPGegPLAj+W/8TaN4IzvnXwCpgGfASEBdp5wy8gvcdQxneFfqNxzpH4BfBTFsNjDjR46qrAhGRCNXQb9GIiMhRKOBFRCKUAl5EJEIp4EVEIpQCXkQkQingpdEL9uB423G2GW9mZ9ZXTSJ1QQEvAs2AYwY8cBowN/SliNQdBbwIPAZ0NrNFZvb7w1eaWU9gjXOu4rDllwX7MF9sZrPqq1iRmtKDTtLoBXvonO68/sirW//fwC7n3HOHLV8KDHfObTazZs7r2lckbOgKXuT4LgDer2b558AkM/svvIEqRMKKAl7kGMwsEWjmnDuiNz/n3K3A/Xg9/y0ys7T6rk/kWBTwIrAbaHqUdecCM6pbYWadnXNfOOceAHZwaBevIr5TwEuj55zLAz4PfmF6+JesI6j+9gzA781saXAg5VnA4lDWKVJb+pJV5BjM7D/Aac4bjEKkQVHAi4hEKN2iERGJUAp4EZEIpYAXEYlQCngRkQilgBcRiVAKeBGRCPX/AasSTF25B7C9AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho.plot()\n", "xl=ax.get_xlim()\n", "ax.set_xlim(xl)\n", "ax.plot(xl,ex0.Peq[0]*np.ones(2),linestyle=':',color='black')\n", "_=ax.plot(xl,ex0.Peq[1]*np.ones(2),linestyle='--',color='grey')" ] }, { "cell_type": "markdown", "id": "b9170049", "metadata": {}, "source": [ "As we see, both spins arive at their thermal polarization using the 'DynamicThermal' option.\n", "\n", "This option may be used in particular to investigate NOE enhancements, or coupled longitudinal relaxation of spins. See $T_1$ and NOE for [solution](../Chapter2/Ch2_T1_NOE.ipynb) and [solids](../Chapter3/Ch3_T1_NOE.ipynb), and the DNP [Overhauser Effect](../Chapter4/Ch4_OverhauserEffect.ipynb)." ] }, { "cell_type": "markdown", "id": "5cd76563", "metadata": {}, "source": [ "### Limitations of 'DynamicThermal'" ] }, { "cell_type": "markdown", "id": "addb0fb7", "metadata": {}, "source": [ "There are some limitations to this approach, due to numerical stability for very fast motions (see [$T_1$ limits](../Chapter2/Ch2_T1_limits.ipynb)), and also because it does not correctly achieve thermalization of the coherences. The latter limitation we demonstrate here. We create a system with a fast-relaxing electron due to dynamics, and add thermalization to it, to see if we can obtain a [contact shift](../Chapter5/Ch5_ContactShift.ipynb) on the nucleus.\n", "\n", "We run the calculation twice, once with a 1 ns correlation time on the motion, inducing only slow electron $T_1$ relaxation, and then with a 1 ps correlation time, inducing fast electron $T_1$ relaxation. Only the latter will cause the proton signal to collapse into a single peak. We will then add thermalization, via `L.add_relax('DynamicThermal')`, but we fail to produce the contact shift, due to incorrect thermalization of the coherences." ] }, { "cell_type": "code", "execution_count": 74, "id": "4586d749", "metadata": {}, "outputs": [], "source": [ "gxx,gyy,gzz=2,2,2.05\n", "ex0=sl.ExpSys(200,Nucs=['1H','e'],vr=0,T_K=50,LF=True,pwdavg='alpha0beta45')\n", "ex0.set_inter('g',i=1,gxx=gxx,gyy=gyy,gzz=gzz)\n", "ex0.set_inter('hyperfine',i0=0,i1=1,Axx=1e6,Ayy=1e6,Azz=1e6)\n", "ex1=ex0.copy()\n", "ex1.set_inter('g',i=1,gxx=gxx,gyy=gyy,gzz=gzz,euler=[0,np.pi/2,0])\n", "\n", "L=sl.Liouvillian(ex0,ex1)\n", "L.kex=sl.Tools.twoSite_kex(1e-9)\n", "\n", "seq=L.Sequence(Dt=5e-11)\n", "rho_1ns=sl.Rho('ez','ez')\n", "_=rho_1ns.DetProp(seq,n=15000)\n", "\n", "L.kex=sl.Tools.twoSite_kex(1e-12)\n", "\n", "rho_1ps=sl.Rho('ez','ez')\n", "_=rho_1ps.DetProp(seq,n=15000)" ] }, { "cell_type": "code", "execution_count": 75, "id": "30b0488a", "metadata": { "scrolled": true }, "outputs": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho_1ns.plot(axis='ns')\n", "rho_1ps.plot(axis='ns',ax=ax)\n", "T1_1ns=6.5e-6\n", "T1_1ps=15.8e-9\n", "ax.plot(rho_1ns.t_axis*1e9,np.exp(-rho_1ns.t_axis/T1_1ns),color='black',linestyle=':')\n", "ax.plot(rho_1ns.t_axis*1e9,np.exp(-rho_1ns.t_axis/T1_1ps),color='grey',linestyle='--')\n", "_=ax.legend(('1 ns motion','1 ps motion',rf'$\\tau_c$={T1_1ns*1e6:.1f} $\\mu$s',rf'$\\tau_c$={T1_1ps*1e9:.1f} ns'))" ] }, { "cell_type": "markdown", "id": "ab9950cf", "metadata": {}, "source": [ "We induce a very slow electron $T_1$ relaxation with the 1 ns motion (6.5 μs), but an electron $T_1$ of 15.8 ns with the 1 ps motion. We next see how this influences the $^1$H lineshape." ] }, { "cell_type": "code", "execution_count": 76, "id": "8faa716b", "metadata": {}, "outputs": [], "source": [ "Upi2=L.Udelta('1H',np.pi/2,np.pi/2)\n", "L.kex=sl.Tools.twoSite_kex(1e-9)\n", "\n", "seq=L.Sequence(Dt=6e-7)\n", "rho_1ns=Upi2*sl.Rho('Thermal','1Hp')\n", "_=rho_1ns.DetProp(seq,n=1000)\n", "\n", "L.kex=sl.Tools.twoSite_kex(1e-12)\n", "\n", "rho_1ps=Upi2*sl.Rho('Thermal','1Hp')\n", "_=rho_1ps.DetProp(seq,n=1000)" ] }, { "cell_type": "code", "execution_count": 77, "id": "eeed38ed", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho_1ns.plot(FT=True,axis='MHz',apodize=True)\n", "_=rho_1ps.plot(FT=True,axis='MHz',apodize=True,ax=ax)" ] }, { "cell_type": "markdown", "id": "eb8b5f88", "metadata": {}, "source": [ "For slow electron relaxation, we obtain two peaks, with different intensities due to different populations of the two electron states. For fast relaxation, the peaks merge into a single peak. This should yield a contact shift, but since the system is not thermalized, no contact shift appears.\n", "\n", "Below, we thermalize the system with `DynamicThermal`, but because this method does not thermalize the coherences, we still do not expect a contact shift." ] }, { "cell_type": "code", "execution_count": 78, "id": "a9723716", "metadata": {}, "outputs": [], "source": [ "L.add_relax('DynamicThermal')\n", "\n", "L.kex=sl.Tools.twoSite_kex(1e-9)\n", "\n", "seq=L.Sequence(Dt=5e-11)\n", "rho_1ns=sl.Rho('zero','ez')\n", "_=rho_1ns.DetProp(seq,n=1000)\n", "\n", "L.kex=sl.Tools.twoSite_kex(1e-12)\n", "\n", "rho_1ps=sl.Rho('zero','ez')\n", "_=rho_1ps.DetProp(seq,n=1000)" ] }, { "cell_type": "code", "execution_count": 79, "id": "41833005", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho_1ns.plot(axis='ns')\n", "rho_1ps.plot(axis='ns',ax=ax)\n", "_=ax.plot(rho_1ns.t_axis[[0,-1]]*1e9,np.ones(2)*ex0.Peq[1],linestyle=':',color='black')" ] }, { "cell_type": "markdown", "id": "f32305f8", "metadata": {}, "source": [ "We first check that the electron z-magnetization is correctly thermalized, as can be seen above." ] }, { "cell_type": "code", "execution_count": 80, "id": "2aa62d84", "metadata": {}, "outputs": [], "source": [ "L.kex=sl.Tools.twoSite_kex(1e-9)\n", "\n", "seq=L.Sequence(Dt=6e-7)\n", "rho_1ns=Upi2*sl.Rho('Thermal','1Hp')\n", "_=rho_1ns.DetProp(seq,n=1000)\n", "\n", "L.kex=sl.Tools.twoSite_kex(1e-12)\n", "\n", "rho_1ps=Upi2*sl.Rho('Thermal','1Hp')\n", "_=rho_1ps.DetProp(seq,n=1000)" ] }, { "cell_type": "code", "execution_count": 81, "id": "6a834326", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho_1ns.plot(FT=True,axis='MHz',apodize=True)\n", "_=rho_1ps.plot(FT=True,axis='MHz',apodize=True,ax=ax)" ] }, { "cell_type": "markdown", "id": "21595e16", "metadata": {}, "source": [ "With slow motion, we obtain two peaks with different peak heights. However, for fast motion, we still do not observe a contact shift, as expected, due to incorrect thermalization of the coherences. \n", "\n", "Finally, we re-build this system with explicit electron relaxation, using Lindblad thermalization, to obtain the correct contact shift. We will explicitly input the 15.8 ns electron $T_1$ that was induced by motion above." ] }, { "cell_type": "code", "execution_count": 82, "id": "9f8ddae2", "metadata": {}, "outputs": [], "source": [ "L=ex0.Liouvillian()\n", "Upi2=L.Udelta('1H',np.pi/2,np.pi/2)\n", "\n", "seq=L.Sequence(Dt=6e-7)\n", "L.add_relax('T2',i=1,T2=T1_1ns,OS=True)\n", "L.add_relax('T1',i=1,T1=T1_1ns,OS=True,Thermal=True)\n", "\n", "rho_1ns=Upi2*sl.Rho('Thermal','1Hp')\n", "_=rho_1ns.DetProp(seq,n=1000)\n", "\n", "# Note: we should use OS=True because we're in the LF for the electron\n", "L.add_relax('T2',i=1,T2=T1_1ps,OS=True)\n", "L.add_relax('T1',i=1,T1=T1_1ps,OS=True,Thermal=True)\n", "\n", "rho_1ps=Upi2*sl.Rho('Thermal','1Hp')\n", "_=rho_1ps.DetProp(seq,n=1000)" ] }, { "cell_type": "code", "execution_count": 83, "id": "eaf9ba6e", "metadata": {}, "outputs": [ { "data": { "image/png": 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8oqpbgUfcbYCXgW2qehFwDfB3IhIJ5tstHrzmw7E8UTFPpUlkUpBNlcmpdEMmAVlrOFEPzoCS+a2/xOZT8YEgPZVLgb2quk9Vk8D9wPaCMtuB+9ThCaBPRNZWqLsduNddvxe4HkBVJ1U17e7vAOyVwwe8jo6eqMTNU2keyRJTCXt4TY0tWV8XqYzm5lEBJ/xlOZXGqUtUROQDVRRbBxzM2z7k7qumTLm6q1X1KIC7XJVn12Uisgt4Cbg1T2Tybb9FRHaKyM6BgYEqvsbixvNUvMEkY5EwCYs7N4dUiQm6PGI2UnEjpDOzPZWI9VPxhXo9lbdVUUaK7Ct8DShVppq6cwuoPqmq5+HY90ci0lGkzN2quk1Vt/X391c65aKn0FOxJsVNpNQEXR7efkvW10X+JF3g3NsmKo1Tl6io6p9UUewQsCFvez1wpMoy5eoed0NkuMsTRex7BZgAzq/CTqMMyYwTr/cS9fFoyDo/Ngsv/GWeSiCkstm5nR9tQMmGqZjIFpGbiu1X1fsqVH0a2CoiW4DDwA3ArxaU2QHcJiL3A5cBI6p6VEQGytTdAdwM3OEuv+vauQU4qKppEdkEnAW8Uen7GeWZLsypmKfSPLzwV7lEfX45o2oyWUWVuZ0fLafSMNW0jsoPdXUAVwHPAmVFxf3nfhvwEBAG7lHVXSJyq3v8LuBB4DpgLzAJfKJcXffUdwAPiMgngQPAR9397wRuF5EUkAV+S1VPVvH9jDLM5FSsSXHTyXkqZYZpyS9nVI0X5spvUhwNi41S7AMVRUVVfzt/W0SWAl+v5uSq+iCOcOTvuytvXYFPV1vX3T+II2yF+79erV1G9RRr/WVNiptEzlMpNaCkzVNfL16YK1rQT8XCX41TT05lEqdfibEImNv6yzyVpuHlSkol6j0PxnIqNZNy7+FoQT8Vu7cbp5qcyveYaXkVwumM+ECQRhnzB+8hmxX+shBBc0hVSNTnPBULf9WKN3DkrM6PoZB1fvSBanIqf5W3ngbeVNVDAdljzDO8ll651l+RMJmszmnjbwRAskKi3lp/1Y3XyXFW50cb+t4Xqsmp/LgZhhjzE89TyR+mBZywmIlKwHj9VEom6nucpSXqa8YTj4hN0uU79faov9tvQ4z5SaJQVNyH0GLPTSA1AaEohKPFj4ejEOmA5Fhz7WoDvPBXtGA6YUvUN069r5p/56sVxrxlJqfiJOq9GSCtBVgTSJaZoMsj1gOJ8ebY00Z4HsmsRH3EPBU/qLdH/TN+G2LMT7ycinkqLSA5DvEl5cvEeyBhnkqt5MJfeTmVaEhIZRSnp4NRL9W0/uoH/hCn1VduLC1V/eUA7TLmCcVaf4F5Kk0hMeqIRjliSxzxMWqimKfi5Vcy2dnzrBi1UY2n8g3gFWAL8FmcoU+eDtAmYx6RSGcRmXmj88JgNv5XE0iYpxIUXu5kdo9659+hDdXSGNWIygpV/SqQUtUfq+pvAJcHbJcxT0ims8QjIUQ8UbHwV9NIjM208CpF3DyVesgN0xKa3fkRsH5YDVKNqKTc5VEReb+IXIwzarCxCEikZ8/jHTNRaR7V5FRi5qnUg+eNxCIznoq9MPlDNZ0f/9wd7+v3gf8O9AL/JlCrjHlDIp0lHg3ntuOWU2keiTGI95YvE7fWX/WQLuKp5PfBMuqnms6P33dXR4B3B2uOMd9IpDPmqbSKxJgl6gMilSmTU7F7uyGsS7RRlmQ6m+ubAvY21zRUXVGpIlGfHAcbs6om0tm5rb/s3vYHExWjLIU5FWv91SSSE4BWl6gHG1SyRgqbyoP1wfKLkqIiIm8Xr8mPsWjxWn95WPirSXghrWoS9WDJ+hpJFIwUAdYHyy/KeSo3A8+IyP0i8nERWdMso4z5gyMqeQ9e2B68puCJRMVEvSs6lqyviURq9ujbYC9MflEyUa+qtwKIyNnAtcDX3FZgjwL/CPxMVS0G0uYk0hm6YjO3iZdfsQcvYBKjzrJiot4bqdg8lVrIeSrR/NCu5VT8oGJORVVfVdW/VtVrgF8GfoozL/yTQRtntJ5kJls07myeSsAkqgx/eaJjnkpN5Ebfzk/Uhx2P3Fp/NUY1/VRyqOoUzrzxc+aON9qTRCqbCwuA9VNpGl74q9pEvTUrrolEOkMkJLPmU7HWX/5grb+MshR6KiJCLGzz1AdOLqdiifogSKRm39dgORW/MFExylLoqYA7T709eMGSa/1VbaLeRKUWEum593Vu7C+7txvCRMUoi+OphGfti0dC1k8laGpO1Fv4qxYKWzVCXpNiC381RMmcioiMAcXGgBZAVbXCK5TRDiRSGfNUWkFiHEIRZ7rgckQ7QcLmqdRIIp2Z1fILIO4m6u3eboxyTYorBHONxUAyMzdMEI+EmLYHL1i8Ye8r9T8WgY6lMD3SHLvahETacipBYeEvoyTZrJLK6JyHryMaZjpl4a9AqWbcL4/OPpg6FaQ1bUeiTPjL5qlvDBMVoyRe08pCT6UzZqISONMj0NFXXVnzVGomkc7MeVkKh4RwSMxTaRATFaMkidTc8ZEAOs1TCZ7pU44HUg0dfU55o2oSqeycnAo4nSGtn0pjBCoqInKNiLwmIntF5PYix0VEvugef1FELqlUV0SWi8jDIrLHXS5z918tIs+IyEvu8peD/G6LgUTGEY5CT6UjGmbKRCVYpoYdD6QazFOpmWLhL7BGKH4QmKiISBi4E2fcsHOBG0Xk3IJi1wJb3c8twJeqqHs78IiqbgUecbcBTgIfVNULcAbD/HpAX23RMOOpFIS/omGmkiYqgTJ1CjqXVVfWRKVmioW/wJlfxUaLaIwgPZVLgb2quk9Vk8D9wPaCMtuB+9ThCaBPRNZWqLsduNddvxe4HkBVn1PVI+7+XUCHiMQD+m6LAi8MUDxRbw9eoNQS/rJEfc0UTungETdPpWGCFJV1wMG87UPuvmrKlKu7WlWPArjLVUWu/RHgOVVNFB4QkVtEZKeI7BwYGKjh6yw+ik1kBNARDVlOJUhSU5Ceri1Rn0lAajpQs9qJUuGveMRyKo0SpKgUa2Bf2JmyVJlq6ha/qMh5wH8GfrPYcVW9W1W3qeq2/v7+ak65aMmN5Fos/GWiEhye11F1+KvPWVqyvmqKDdMCELdGKA0TpKgcAjbkba8HjlRZplzd426IDHd5wiskIuuBbwM3qerrPnyHRc2Mp1LQ+ivmiIpqVTpv1IonDlW3/nIT+pZXqZpEqnhOxbzwxglSVJ4GtorIFhGJATcAOwrK7ABucluBXQ6MuCGtcnV34CTicZffBRCRPuB/A3+kqj8L8HstGrzxvYq1/lK1IcIDo1ZPxRMfy6tUTSJdvEmxNZdvnMBERVXTwG3AQ8ArwAOquktEbhWRW91iDwL7gL3Al4HfKlfXrXMHcLWI7AGudrdxy58B/EcRed79FMu3GFWSLDKRETiiAjCdNFEJhKlhZ1l1TsUtZ55KVaQzWdJZLZpTsUYojVPTJF21oqpzJvRS1bvy1hX4dLV13f2DwFVF9v858OcNmmzkUWzKVXDe5gCmUhmWEm26XW1PzeGvvtn1jLKUatUIFv7yA+tRb5SklKfSGXO2LVkfEDUn6pfOrmeUpVT/K7COvX5gomKUxMupxKOzwwQdbtjA3ugCYmoYEIhX2aPeE5/JwcBMaiemS9zXYOEvPzBRMUpSMqcSmwl/GQEwfQo6eiFU5eMZjjghMBOVqph0R4PoihURlUiYhN3XDWGiYpSkUk5l2oZqCYZahmjx6F4JkycDMafdmEx4ojI3pdwRDdnLUoOYqBglSVRq/WVTCgfD1HD1Lb88ulaap1Ilk8k0AN1FPJXOaJh0Vklbc/m6MVExSlJKVHKtv6xJcTBMDEB3jaM9dK2ACROVavDCX53Fwl+5Fya7t+vFRMUoyWQiTVcsTCg0e9Sc/CbFRgDUIyrdK8xTqRJPVLrjxcNfgI3C3QAmKkZJJpKZ4nFnr0mxG0YwfETVEZWeOjyVyUGnvlGWCfe+LZqoj1rLxkYxUTFKMplM0x2f++D1uG944wl78HxnegQySeiucTCIrpWQTUFiNBi72oipZLlEvXO/JyxfWDcmKkZJJhLpog9eZzRMSJzjhs9MuC246smp5Nc3SlKNp2L5wvoxUTFKMpHI0FPEUxERumMRxk1U/GfCHXS71vBX90pnOTnkrz1tyFQyQ0iK96jvtJaNDWOiYpRkMlncUwEnyWmeSgBMuBPH1eypLHeW1lelIhOJDN2xCCJzp23yhiCatER93ZioGCWZSGaK5lQAuuPhXBjB8JFx11OpNafilR8/Ub6cwVQqXbQ5Mcy0CJu0F6a6MVExSjKRSNNdwlPpiUcsUR8EEycBmcmRVEvPamc5dsx3k9qNiUSmaHNiIHe/W2i3fkxUjJJMJNKlHz4LfwXDxAknlBWucVaKSMxpATZ2NBi72ojJZCaXOynEu9/t3q4fExWjKKrKZDJTtIUMmKgExsRA7aEvjyVrYPy4v/a0IaWaygO5/ROWU6kbExWjKIm0MzteKU/FCX+ZqPjO+MBMS65aWbLGPJUqmExm6CwR1o1HwkTDYi9MDWCiYhQlN5RFSU8lbA9eEIweht7T6qu7ZI3lVKpgMpkueV+D0ynS7u36MVExiuI9VF1lcyoWIvCVbAZGj8DS9fXV73HDX1n7u5RjIlF8+CEPa4TSGCYqRlEmcsODF3/4ejuiJDNZG87CT8aPg2agd1199ZesAc3O9HUxijIylWJpZ7Tk8e54ODc8vlE7JipGUTwvpFRCs9d9KEemUk2zqe0ZOews6/VUlqx1lhYCK0k6k2U8kS4rKl02WkRDmKgYRfHCX6US9d5DOWqi4h8jB51lvZ6Kl4sZOeSPPW3I2LRzX/d2lg9/WU6lfkxUjKJ4HkipN7ql5qn4z6jnqdQpKn2bnOWpA/7Y04ZUuq/Ba4RiYd16MVExinLKffj6TFSax8hhiPXUPpWwR9dyiHabqJShOlGx8FcjmKgYRfHCWr0VROXUpImKb4weckJfRQY6rAoR6NtoolKGkQr3NTj3toV168dExSjKyFSKjmgoN79EIeapBMDI4fpDXx7LNpmolGF0urKnsrQzylgiTTpjc6rUg4mKUZRTk8myD15vh5PoNFHxkeE3HE+jEcxTKUvOU+koLyoAo9MWAqsHExWjKCNTKfo6YyWPR8IheuIRExW/mByCqSFYcUZj5+nbCIkRmDrli1ntRjU5FfPCG8NExShKpQ5i4Dx8llPxicHXnWWjorJss7Mc3t/YedqU0ak0sXCIjmjpf319XSYqjRCoqIjINSLymojsFZHbixwXEfmie/xFEbmkUl0RWS4iD4vIHne5zN2/QkQeFZFxEfmbIL/XYmBkKl02mQmwckmck+OJJlnU5gzudZaNisqKrc7y5N7GztOmjEyl6O0sPuujh3kqjRGYqIhIGLgTuBY4F7hRRM4tKHYtsNX93AJ8qYq6twOPqOpW4BF3G2Aa+I/AHwT1nRYTI5PJ3BtbKfp7YpwcTzbJojZn6HWQ8Exfk3pZvsU5z8nd/tjVZgxNJFjeXTqsC/ktG+3erocgPZVLgb2quk9Vk8D9wPaCMtuB+9ThCaBPRNZWqLsduNddvxe4HkBVJ1T1pzjiYjRINeGvlT3mqfjG4F6n5Vak/D+8ikTiTgjMRKUoA2MJVvbEy5bptdEiGiJIUVkHHMzbPuTuq6ZMubqrVfUogLusaUYjEblFRHaKyM6BARt4rxjJdJaJZKYqURmaSJLNapMsa2MG98Lyt/hzrpVnwsk9/pyrzTg5nqR/SXlR8RqoDFu+sC6CFJViQcvC/z6lylRTty5U9W5V3aaq2/r7+/04ZdsxOOF4H5UevhU9MTJZzfW+N+okm3FyICvP9Od8K7c6ImVD4M9hYCxBfwVPJRYJsaQjwqB54XURpKgcAjbkba8HjlRZplzd426IDHd5wkebDeDEqCsqFR4+L4xgIbAGGdwL6SlYc4E/5+s/GzIJGLIWYPlMJNJMpTKsrPCyBM69b/nC+ghSVJ4GtorIFhGJATcAOwrK7ABucluBXQ6MuCGtcnV3ADe76zcD3w3wOyxKBsaq81RyojJmotIQx15yln6JineeYy/4c742IXdfV3hZAssXNkLp8Z8bRFXTInIb8BAQBu5R1V0icqt7/C7gQeA6YC8wCXyiXF331HcAD4jIJ4EDwEe9a4rIG0AvEBOR64H3qurPg/qO7coJ9+Fb1Vv+4etf4sSeB+zha4xjL0I45l/4q/9sCEXh6Itw/kf8OWcb4N2n1XgqK5fEeO3YWNAmtSWBiQqAqj6IIxz5++7KW1fg09XWdfcPAleVqLO5AXMNF++NbkV3+YdvzdJOAI6OWIO7hjj2kiMEjbb88ojEYNU5cNQ8lXxO1uip/Gx8MGiT2hLrUW/MYWB8mmVdUWKR8rdHTzzC0s4oh4Ynm2RZG6LqeBRrLvT3vGsvdDwgtZZ5Ht7LTyUPHBxRGZlKkUzboJK1YqJizOHEaIJVSzqqKrt+WSeHh6cCtqiNGd4Pkydh3cX+nnfdW2FyEIb2+XveBcyh4Sk6o2FWVOj8CLDKDZGdGDMvvFZMVIw5nBhLVEzSe6zr6+TwKROVunnzcWe58Qp/z+ud78Dj/p53AXNweJINyzvLDtHicVqfE9q1F6baMVEx5nBoeIp17kNViXXLOjk0PIVamKU+DjzmzPTYf7a/5+0/CzqXz4iWwcGhSTYs66qq7LplrqjYC1PNmKgYs5hMpjk5nmDjiiofvr5OJpMZ631cL28+DhvfDiGfH0UR57wHHvP3vAsUVeXw8BTrl1X5smSeSt2YqBizODjkPEQbllcnKptXdAPwxuBEYDa1LSOHnYEkN/kc+vLYdIWTUxk5FMz5FxAjUynGEumq7+uOaJiVPTHzVOrARMWYxcEhpyXXhirf6Lau7gFg7/HxwGxqW/Y85Cy3vjeY82+92lnufiiY8y8g9p10Xno2uS9B1WD5wvowUTFmccAVlY1VvtGtX9ZFPBJizwnrKFYzux9yhrrvPyuY86880xmx2ESF3W5HxrNWL6m6zvplXbmXLKN6TFSMWbw5OEF3LFxxzgmPcEh4S38Pe06Yp1ITyUnY92M48xon/xEEIs759//Yud4i5rXjY3RGw1XnVADesqqHA0OTTKdsYM5aMFExZvHqsTHOXLOkqmaXHltX9+TeBI0qee1BZxDJcz4Q7HXO/gCkp53rLWJ2Hx/jzNU9hEI13Neresgq7BuwfGEtmKgYOVSVV4+Ncfaa3prqXbBuKUdGpnPDuxhV8MK3YOkG2PTOYK+z6R3Qux5euD/Y68xjVJVXj45xZg2hLyBX3kK7tWGiYuQ4PppgZCrF2Wtqe/gu2tAHwPMHT/lvVDsydgxe/yFc+C/9b0pcSCgEF37Mud7YsWCvNU95Y3CSwYkkl2xaVlO9zSu7CIeEPdYIpSZMVIwcrxwbBeCsGkXl/HVLiYSE5w4MB2FW+7HzHtAsXPSrzbnexb/mXO/przbnevOMnW8MAbCtRlGJR8Kc0d/DS4dHgjCrbTFRMXI888Yw4ZBwwbqlNdXriIY577Rento/FJBlbURyAp66G856P6zwafrgSqx4C5x1LTz9FUgtviayO98Ypq8rylv6e2que8mmPp47MGxTZteAiYqR46n9Q5y/bind8dpnRHjX1n6eO3iK0WnrWV+WZ74GU8Pwzt9t7nWv+G2YGnKEZRGhqjy+b5Btm5bVlKT3uHjjMkan0+w7aSGwajFRMQCYTmV4/tApLtuyvK76v3hmP5ms8rM9J322rI2YHIIffx5OvxI2XNrca2+6At5yFfzzXzmitkjYfXycA0OT/PLZq+uq/1Y3ZPbU/sXzmzWKiYoBwLNvDpNMZ7l0c32icvHGPpZ3x/j+i0d9tqyNePRzkBiF932uNde/+rMwPQI//IvWXL8FPLTrGCLwnnNX1VX/9JXdrOvr5EevnfDZsvbFRMUA4AcvH6MzGuYdZ6ysq340HOKDF67l4VeOWwisGPt+BE9/Gd72KVh9XmtsWHMBXHarY8f+n7TGhiaiqux44QiXbFxW9fxAhYgIV57Vz0/3niSRtk6Q1WCiYpDJKv+46xjvPrufzli47vN86JL1JNNZvv3sYR+tawPGT8C3/7UzbMp7PtNaW676T7D8dPiHT7V9E+Mn9g2x98Q4N7xtQ0Pnufrc1UwmMzz66oBPlrU3JioG/7x7gIGxBO+/4LSGzvML65dyycY+vvyTfaQzNg0r4LT2+ubHYPoUfOQrEKtuTLXAiHXBx74O06Nw/79y7GtTvvKTfSztjPLBX2jsvn7nGStZtSTO/3rmoE+WtTcmKgb3/Gw/q3vjvPe8+pKZHiLCb115BoeGp/jWUwd8sm4BkxiDb/5LOPoCfOSrsPYXWm2Rw5rz4cN/B0eehW98rC2F5cl9gzzy6glu+cXT6YjW730DRMIhPrptPT989QT7BqwVWCVMVBY5T78xxE/2nOSmt28mGm78drjqnFW844wVfP6h1zgxuojn9z51EL72AWc63w/dDWdf12qLZnPOB+HDX3Ym8fr/r3XsbROmUxn+ZMcu1vR28Bvv2OLLOT9+xRai4RB3Pvq6L+drZ0xUFjHpTJbPfm8Xa5d28Il3bPblnCLCn24/n1Qmy29/6zlSiy0Mpgo//y7c9U4YfB1u+CZc+NFWW1WcC34FbrwfhvbD3b8Eu77j2L+AUVU+9+ArvHpsjM99+PyGcoT59C+Jc/MVm/mH5w7xzJvWvLgcJiqLmP/28G5ePjzKH7//HLpitXd4LMVb+nv4yw9fwJP7h/i9B15YPPmVgdfgGx+FB26Cvo3wmz+GM9/XaqvKc+b74FOPQu86+J83w7duhBOvtNqquvnbH73OfY+/ySffuaXuviml+J2rtrK2t4Pff+B5RqashWMpTFQWKd988gB/+6PXufHSDXzgwsYSmcX40MXruf3as/neC0f4xNeeZnC8TUcwVoUDT8L/+HW48zIn3PXev4BP/bB5w7A0ysozHGG5+s/gjZ/A374d/ucn4MATC8ZzSaaz/IfvvMR/eeg1rr/oNP74unN8v0Z3PMIXbryYw6emuPXrzzCZTPt+jXZAdIHcNEGwbds23blzZ6vNaCqZrPLFR/bwhUf28O6z+vnSr7214URmOb711AH+ZMculnZG+XfvO4uPXLK+ruEy5hWqcPxleO0fnSHsh16H+FK49FNw+b+G7vr6+swLJofgsf8OT30ZkmNOM+gLPgZnXQOrzw9uQrE6UVV+tneQz3xvF3tPjPObv3Q6/+59ZxMO8B77znOH+b0HnueC9X3c+asXs35Zi1v0tQAReUZVtxU9ZqKyeETl6TeG+Iv//QrPHzzFhy9Zx19++ALikeAExWPXkRH+w3de5rkDp9i0ootfv3wT2y9aR/+SeODX9oVMGgZegUM74dDT7jDy7sgBm97hjDZ87naI1za687wmMQ4//w48+3U4+ISzb+kG2Pwu2PA2WH8prDoHQsHfP8UYm07x8M+Pc+9jb/DCoRE2LO/kT7efz7vPqq/nfK08tOsYv//ACwjwO+/Zyq9dvinQl7P5holKCRaDqAyMJfjhq8e5/+mDPHfgFKuWxPn3153D9Reva6odWbeD5T0/3c/ON4cRgYs39PGurf1ctLGPi9b3sazKKYwDQRUmTsLoITh1AE7uhoHdzvLkbki50/F2LoMtvwhb3wtnvAeWrGmdzc1i7DjseciZ6/7A4zA56OyPdjmeTP9ZM8ulG2Dpeuha4atXM5lM8/Mjozz1xhBP7R/isb2DJDNZNq/o4v951+n8ylvXN/2f+sGhSf79t1/iJ3tOsqI7xocuXsf1F6/j3LW9C98br0DLREVErgG+AISBr6jqHQXHxT1+HTAJfFxVny1XV0SWA/8D2Ay8AXxMVYfdY38EfBLIAP+vqj5Uzr52EhVVZWQqxYGhSV45OsrLh0d57uAwLx925kg5Y1UPN166kRsv3eBrUr4eXjs2xkO7jvFPrxznpcMjubD9mt4ONq/sYsvKbjat6Gbt0g5W9sTdT4y+rlh1YY1sBpLjTv+LxLgTxpkadkI7k0POaL2Tg876+AkYPQyjRyBTkPfpXQ/9Z8LKs2DdJbDurU5v9HkWAmoqqjC0z/HajjwHJ19zxHf00Oxy4Tj0nuYITM8q6FwOXcvzlsuc9c4+stFuxrIxRtIxTownOToyzdGRKY6OTPPm4CS7j49xaHhmyP4zVvXwrq0r+cCFp3Hxhr6W/wN//PVBvvbYfh555QTprLK8O8bbT1/Beet6OXvNEs5cvYS1SzsDDck1m5aIioiEgd3A1cAh4GngRlX9eV6Z64DfxhGVy4AvqOpl5eqKyOeBIVW9Q0RuB5ap6h+KyLnAt4BLgdOAfwLOVNWSA/bMB1HJZpVUNks6o6QzM+tTqQyTyTRTyQyT7mcqlWYikeHUZJKhiRRDEwmGJlOcGJ3m8PAUY4mZxOGSeITz1vXyzjNWcuVZqzjvtN6ZeedV3U/W+ZC3rtnZx1SLHC8s47buymYgm877VNpOM51McnBwlMMnxxkYneDU+BTjExOkktPEJUWcNHGSxEgTlxQ9kQxdoTSdkqYjlKaDFJ0k6GCajuwksewUsWz5/jGKkI4tJd2xjHTHCtI9p5HuWUu65zQyPWtJL9lAetnpEOshHBJCAiERxF06HwiFZtZFZsqFQ7PLNhtVRXHyZ6qQVXU/zrFs3r6Z4869WKx8Rt17M5MlnVVS6SyprJLOZElllHQ2i06P0TG6n/jEUTqmjhKfPEbH5FG6po/RlRqiMz1CR2acEOX/30xpjAk6mNI4U9JBJtJFKN5NtKOHrq4u+pZ00xHvhEgMwjEIR91l4SdvfyQGoQhICCTszIYpYSd0J2Fnv7fuHZu1L3+7oG4olNs3OJnmn/cM8ti+QZ7eP8zhkWmcp0cIh0Ks6omxamknq3s76e/tYElHhCUd0dnLeIR4JEwsEsp9omEhHp7ZNx/EqZyoBPnKeimwV1X3uUbcD2wHfp5XZjtwnzrK9oSI9InIWhwvpFTd7cCVbv17gR8Bf+juv19VE8B+Ednr2vC4319s/8uPs+TvfxXndsnDFWiZ9eB4+7wtRTRv3d3v1YkAUZROYMWsq86cU9xPSBQRcbbDEOr29jv/5OSEwgmFn2XnisQ8oQPY6n5mEXUW2VCMTDhOWqKkiJEkQlJiJDRKgggTGmUg282YdjCaiTOSjTOW7WAC96PO8pT2MMwShrWHEXrITodgtJRVw8AzAX3jdmeV+3FGD4iFQ3REQ3TFInR3wIrINP3hcVZFJlkdnWRleIql4SS94STdoQS9oQRLQilWyzSx7JTjbSYnITUM08dhIgmZFGSSjmfprWdb3xJrBfAh9wM4N3c+SWDA/eSRVcmJj/cfwdvO/2+iCIlZ/10EFZn1H2b2OYosZWb9zZW/xCWfvreBb1ycIEVlHZDfTfcQjjdSqcy6CnVXq+pRAFU9KiJeZm4d8ESRc81CRG4BbgHYuHFjDV9nhmjXMl5d8nYQ708Zylv3VsRbOOu5pfeWGyKEOC9AEnKEIBTKe9sNEQkLkXCYaEhm1sNCLBIi4iVIi70J5++T0MwHmb0tIVehypWRgmW5MiHnjXDWJ1z7djgGkTiEY87bPo7GdFb598lknbfqZCbrvFVn8rYzWVJpza0n087Se3vPf5Of/aY/czyTnVs291afnVu2FdGyGe9JCIc8T2vGm8o/PscTK1I+EhKi4RDRsHNfRsNCJOStu/vdMpGw0BEN0xEJEfFhlIaqyGZdoSkiOumEIzrei1U2A5pxl1l3PVtkX2Z2+aJ1C/Z5//JzHj5F9jlLVfe+TGdIpjIk0hmSmSzZTJZMNks26ywzCtnctqLZLBlVNDtzPnXPl7uOu2/uNZnZXnF+IH+KIEWl2KNU+Ipcqkw1deu5Hqp6N3A3OOGvCucsyvrTz2b9732znqpGEwiHhHAovKha4yx6QiEIdUC0viHuW4EAMffTTgT5GnEIyB9zej1wpMoy5eoed0NkuEtv9pxqrmcYhmEESJCi8jSwVUS2iEgMuAHYUVBmB3CTOFwOjLihrXJ1dwA3u+s3A9/N23+DiMRFZAtOmP6poL6cYRiGMZfAwl+qmhaR24CHcJoF36Oqu0TkVvf4XcCDOC2/9uI0Kf5Eubruqe8AHhCRTwIHgI+6dXaJyAM4yfw08OlyLb8MwzAM/7HOj23ST8UwDKNZlGtSbANKGoZhGL5homIYhmH4homKYRiG4RsmKoZhGIZvLOpEvYgMAG+26PIrgZMtuna9LESbwexuJgvRZjC7a2WTqvYXO7CoRaWViMjOUq0n5isL0WYwu5vJQrQZzG4/sfCXYRiG4RsmKoZhGIZvmKi0jrtbbUAdLESbwexuJgvRZjC7fcNyKoZhGIZvmKdiGIZh+IaJimEYhuEbJio+IyLXiMhrIrJXRG4vcvzfisjz7udlEcmIyHL32Bsi8pJ7rKkjXVZh95UiMpJn+3+qtm4Lbf5XIvKi+3lMRH4h79h8/q1FRL7oHn9RRC6ptm4zEJHlIvKwiOxxl8uKlNkgIo+KyCsisktEfifv2GdE5HDevXTdfLHbLVf03qi2frNtFpGz8n7L50VkVER+1z3W/N9a3WlP7dP4B2eY/teB03EmdHsBOLdM+Q8CP8zbfgNYOR/tBq4Evt/od26yzVcAy9z1a4EnF8hvfR3wA5zJAS/37G7Vb13kO3weuN1dvx34z0XKrAUucdeXALs9W4HPAH8wH+0ud29UW78VNhfcX8dwOie25Lc2T8VfLgX2quo+VU0C9wPby5S/EfhWUywrT612+1W3ESpeV1UfU9Vhd/MJnNlAW001v9d24D51eALoE2eW01b91oVsB+511+8Fri8soKpHVfVZd30MeAVY1ywDS1DR7oDr10Ot17wKeF1VWzVSiImKz6wDDuZtH6LEgyQiXcA1wN/n7Vbg/4jIMyJyS2BWzqVau98uIi+IyA9E5Lwa6/pNrdf9JM7bv8d8/q1LlWnVb13IanVmaMVdripXWEQ2AxcDT+btvs0N7d3TjDCSS7V2l7o3avrePlHrNW9g7otqU3/rwGZ+XKRIkX2l2mx/EPiZqg7l7XuHqh4RkVXAwyLyqqr+s+9WzqUau5/FcanH3bjsd3CmbK7lO/tJ1dcVkXfjiMo783bP59+6VJmm/dYi8k/AmiKH/rjG8/TgvDj9rqqOuru/BPwZju1/BvxX4Dfqt3bW9fywu6n3ho+/dQz4F8Af5e0O7LcuhYmKvxwCNuRtrweOlCg7541CVY+4yxMi8m2ccEcz/tFVtDvvHwKq+qCI/K2IrKymbkBUdV0RuRD4CnCtqg56++fzb12mTKyKur6gqu8pdUxEjovIWlU96oblTpQoF8URlG+o6j/knft4XpkvA9+fT3aXuTeqqt8Km12uBZ7N/32D/K1LYeEvf3ka2CoiW9y3hhuAHYWFRGQp8EvAd/P2dYvIEm8deC/wclOsrsJuEVkjIuKuX4pz7wxWU7eFNm8E/gH4dVXdnbd/Xv/W7vZN4nA5MOKGPlr1WxeyA7jZXb+ZvPvYw71Xvgq8oqr/reDY2rzND9G8374au8vdGxXrB0At15yTo23Jb93MVgGL4YPTcmc3TiudP3b33Qrcmlfm48D9BfVOx2nN8wKwy6s7X+wGbnPtegEn6X1FubrzxOavAMPA8+5n5wL5rQW40z3+ErCt1b91gf0rgEeAPe5yubv/NOBBd/2dOCGXF/N+/+vcY193v9eLOP80184ju0veG6Xqt9pmd7sL5yVvaUH9pv/WNkyLYRiG4RsW/jIMwzB8w0TFMAzD8A0TFcMwDMM3TFQMwzAM3zBRMQzDMHzDRMUwDMPwDRMVwzAMwzdMVAyjRYjI34nIO4rsVxH5et52REQGROT77vZ4QfmPi8jfBG+xYVTGRMUwWsdlOKMTFDIBnC8ine721cDhplllGA1gomIYPiMifSJyLG/7GXe8t/wy5wC7VTVT4jQ/AN7vrlc9746I3Jo3y99+EXm0jq9gGHVjomIYPqOqp4Bud5RecMaRurCg2LXAP5Y5zf3ADSLS4dbNn4ukM3/6WOBP8659l6peBLwNZ7TjWYM5GkbQ2ND3hhEMx3HmyDgInO1u5/M+4BOlKqvqi+7kVjcCDxYcnnKFA3ByKsC2gjJfwJmq+nt12G4YdWOiYhjBcAQ4TUSuAE7q7KH3u4A+deftKMMO4K+AK3FGq60KV2Q24YwsbRhNxUTFMILhCM584tfgJNrzeTdQTa7jHpy5VF4SkSuruaiIvBX4A+Bdqpqt1ljD8AvLqRhGMBwGfgX4F6p6suBYpXwKAKp6SFW/UON1bwOWA4+6OZev1FjfMBrC5lMxjCYjIs8Cl6lqqtW2GIbfmKgYhmEYvmHhL8MwDMM3TFQMwzAM3zBRMQzDMHzDRMUwDMPwDRMVwzAMwzdMVAzDMAzfMFExDMMwfOP/AhD7YJyDKBxKAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho_1ns.plot(FT=True,axis='MHz',apodize=True)\n", "_=rho_1ps.plot(FT=True,axis='MHz',apodize=True,ax=ax)" ] }, { "cell_type": "markdown", "id": "d0d96251", "metadata": {}, "source": [ "We obtain a very similar result as before, *however*, now the averaged line has been shifted towards the large peak, which is brought about by having the correct thermalization behavior." ] }, { "cell_type": "markdown", "id": "cf50f69a", "metadata": {}, "source": [ "## Summary" ] }, { "cell_type": "markdown", "id": "23ebccf0", "metadata": {}, "source": [ "### 1. Basic relaxation can be included using:\n", "```\n", "L.add_relax('T1',i=...,T1=...)\n", "L.add_relax('T2',i=...,T2=...)\n", "L.add_relax('recovery') # Optional for thermalization\n", "```\n", "### 2. If quantization axis for a spin is tilted, use:\n", "```\n", "L.add_relax('T1',i=...,T1=...,OS=True,Thermal=True) #Thermal adds thermalization\n", "L.add_relax('T2',i=...,T2=...,OS=True)\n", "```\n", "### 3. If the quantization axis is not tilted, but the polarization varies, use:\n", "```\n", "L.add_relax('T1',i=...,T1=...)\n", "L.add_relax('T2',i=...,T2=...)\n", "L.add_relax('recovery',OS=True) # Orientation-specific polarization\n", "```\n", "### 4. If relaxation is induced explicitely by dynamics, use:\n", "```\n", "L.add_relax('DynamicThermal')\n", "```\n", "*`DynamicThermal` will not produce correct thermalization of coherences!*" ] }, { "cell_type": "code", "execution_count": null, "id": "5a5639ad", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 5 }