docs/tutorials/1_TB_Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "64a1494c-8896-4f83-b2a7-d36e3fa4ff77",
   "metadata": {},
   "source": [
    "# Tight-binding models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "311fbc5e",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/dehe1011/QuantumDNA/blob/main/docs/tutorials/0_TB_Models.ipynb)\n",
    "\n",
    "This notebook demonstrates how to utilize predefined tight-binding models and create custom models and parameters. It includes visualizing the Hamiltonian matrix derived from the selected model and performing a Fourier analysis on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ab9c849a-381d-4601-9a26-1482d46e2a97",
   "metadata": {},
   "outputs": [],
   "source": [
    "# %pip install qDNA\n",
    "# from qDNA import ROOT_DIR\n",
    "\n",
    "# This can be used alternatively if you cloned the GitHub repository\n",
    "import os\n",
    "ROOT_DIR = os.getcwd()[:os.getcwd().rfind('QuantumDNA')]+ 'QuantumDNA'\n",
    "os.chdir(ROOT_DIR)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a11a543",
   "metadata": {},
   "source": [
    "# Predefined tight-binding model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "78d29e7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qDNA import DNA_Seq, TB_MODELS_PROPS\n",
    "from qDNA.model import TB_Model, TB_Ham\n",
    "from qDNA.tools import get_config"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "050a024a",
   "metadata": {},
   "source": [
    "In this chapter we want to use predefined tight-binding models. All we have to provide as an input is the upper strand of the DNA sequence and the name of the predefined tight-binding model. We show all available predefined models with their properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "432edd89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'WM': {'backbone': False, 'double_stranded': False, 'num_strands': 1, 'diagonal_hopping': False}, 'LM': {'backbone': False, 'double_stranded': True, 'num_strands': 2, 'diagonal_hopping': False}, 'ELM': {'backbone': False, 'double_stranded': True, 'num_strands': 2, 'diagonal_hopping': True}, 'FWM': {'backbone': True, 'double_stranded': False, 'num_strands': 3, 'diagonal_hopping': False}, 'FLM': {'backbone': True, 'double_stranded': True, 'num_strands': 4, 'diagonal_hopping': False}, 'FELM': {'backbone': True, 'double_stranded': True, 'num_strands': 4, 'diagonal_hopping': True}, 'FC': {'backbone': True, 'double_stranded': True, 'num_strands': 4, 'diagonal_hopping': True}}\n"
     ]
    }
   ],
   "source": [
    "# input \n",
    "upper_strand = 'GCG'\n",
    "tb_model_name = 'ELM'\n",
    "\n",
    "print(TB_MODELS_PROPS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74f9ae87",
   "metadata": {},
   "source": [
    "First we define an instance of DNA_Seq and print all its attributes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ab322af3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'upper_strand': 'GCG',\n",
       " 'lower_strand': 'CGC',\n",
       " 'methylated': True,\n",
       " 'tb_model_name': 'ELM',\n",
       " 'tb_model_props': {'backbone': False,\n",
       "  'double_stranded': True,\n",
       "  'num_strands': 2,\n",
       "  'diagonal_hopping': True},\n",
       " 'backbone': False,\n",
       " 'double_stranded': True,\n",
       " 'num_strands': 2,\n",
       " 'num_sites_per_strand': 3,\n",
       " 'tb_dims': (2, 3),\n",
       " 'complementary_base_dict': {'A': 'T', 'T': 'A', 'G': 'C', 'C': 'G', 'c': 'G'},\n",
       " 'dna_seq': ('GCG', 'CGC')}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dna_seq = DNA_Seq(upper_strand, tb_model_name)\n",
    "# print all attributes of the DNA_Seq instance\n",
    "dna_seq.__vars__()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d82c430",
   "metadata": {},
   "source": [
    "Then we create an instance of TB_Model and again print all its attributes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f61e8044",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'verbose': False,\n",
       " 'tb_model_name': 'ELM',\n",
       " 'tb_dims': (2, 3),\n",
       " 'num_strands': 2,\n",
       " 'num_sites_per_strand': 3,\n",
       " 'num_sites': 6,\n",
       " 'tb_model_props': {'backbone': False,\n",
       "  'double_stranded': True,\n",
       "  'num_strands': 2,\n",
       "  'diagonal_hopping': True},\n",
       " 'tb_config': [('E', '(0, 0)', '(0, 0)'),\n",
       "  ('E', '(0, 1)', '(0, 1)'),\n",
       "  ('E', '(0, 2)', '(0, 2)'),\n",
       "  ('t', '(0, 1)', '(0, 0)'),\n",
       "  ('t', '(0, 2)', '(0, 1)'),\n",
       "  ('E', '(1, 0)', '(1, 0)'),\n",
       "  ('E', '(1, 1)', '(1, 1)'),\n",
       "  ('E', '(1, 2)', '(1, 2)'),\n",
       "  ('t', '(1, 0)', '(1, 1)'),\n",
       "  ('t', '(1, 1)', '(1, 2)'),\n",
       "  ('h', '(0, 0)', '(1, 0)'),\n",
       "  ('h', '(0, 1)', '(1, 1)'),\n",
       "  ('h', '(0, 2)', '(1, 2)'),\n",
       "  ('r+', '(0, 0)', '(1, 1)'),\n",
       "  ('r+', '(0, 1)', '(1, 2)'),\n",
       "  ('r-', '(0, 1)', '(1, 0)'),\n",
       "  ('r-', '(0, 2)', '(1, 1)')],\n",
       " 'tb_basis': ['(0, 0)', '(0, 1)', '(0, 2)', '(1, 0)', '(1, 1)', '(1, 2)'],\n",
       " 'eh_basis': [('(0, 0)', '(0, 0)'),\n",
       "  ('(0, 0)', '(0, 1)'),\n",
       "  ('(0, 0)', '(0, 2)'),\n",
       "  ('(0, 0)', '(1, 0)'),\n",
       "  ('(0, 0)', '(1, 1)'),\n",
       "  ('(0, 0)', '(1, 2)'),\n",
       "  ('(0, 1)', '(0, 0)'),\n",
       "  ('(0, 1)', '(0, 1)'),\n",
       "  ('(0, 1)', '(0, 2)'),\n",
       "  ('(0, 1)', '(1, 0)'),\n",
       "  ('(0, 1)', '(1, 1)'),\n",
       "  ('(0, 1)', '(1, 2)'),\n",
       "  ('(0, 2)', '(0, 0)'),\n",
       "  ('(0, 2)', '(0, 1)'),\n",
       "  ('(0, 2)', '(0, 2)'),\n",
       "  ('(0, 2)', '(1, 0)'),\n",
       "  ('(0, 2)', '(1, 1)'),\n",
       "  ('(0, 2)', '(1, 2)'),\n",
       "  ('(1, 0)', '(0, 0)'),\n",
       "  ('(1, 0)', '(0, 1)'),\n",
       "  ('(1, 0)', '(0, 2)'),\n",
       "  ('(1, 0)', '(1, 0)'),\n",
       "  ('(1, 0)', '(1, 1)'),\n",
       "  ('(1, 0)', '(1, 2)'),\n",
       "  ('(1, 1)', '(0, 0)'),\n",
       "  ('(1, 1)', '(0, 1)'),\n",
       "  ('(1, 1)', '(0, 2)'),\n",
       "  ('(1, 1)', '(1, 0)'),\n",
       "  ('(1, 1)', '(1, 1)'),\n",
       "  ('(1, 1)', '(1, 2)'),\n",
       "  ('(1, 2)', '(0, 0)'),\n",
       "  ('(1, 2)', '(0, 1)'),\n",
       "  ('(1, 2)', '(0, 2)'),\n",
       "  ('(1, 2)', '(1, 0)'),\n",
       "  ('(1, 2)', '(1, 1)'),\n",
       "  ('(1, 2)', '(1, 2)')]}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tb_model = TB_Model(dna_seq.tb_model_name, dna_seq.tb_dims)\n",
    "# print all attributes of the TB_Model instance\n",
    "tb_model.__vars__()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "707df3f4",
   "metadata": {},
   "source": [
    "To create the tight-binding Hamiltonian from the tight-binding model that we just defined, we can first specify some keywords. We print the default values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "96e49cf1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'source': 'Hawke2010',\n",
       " 'description': '2P',\n",
       " 'particles': ['electron', 'hole', 'exciton'],\n",
       " 'unit': 'rad/ps',\n",
       " 'interaction_param': 0.0,\n",
       " 'relaxation': True,\n",
       " 'nn_cutoff': True}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define the keyword arguments for the tight-binding hamiltonian\n",
    "ham_kwargs = dict()\n",
    "\n",
    "# default keywords: \n",
    "get_config()['ham_kwargs_default']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88e4cdcc",
   "metadata": {},
   "source": [
    "We create an instance of TB_Ham and again print all its attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1283f65e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'ham_kwargs': {'source': 'Hawke2010',\n",
       "  'description': '2P',\n",
       "  'particles': ['electron', 'hole', 'exciton'],\n",
       "  'unit': 'rad/ps',\n",
       "  'interaction_param': 0.0,\n",
       "  'relaxation': True,\n",
       "  'nn_cutoff': True},\n",
       " 'verbose': False,\n",
       " 'dna_seq': DNA_Seq(GCG, ELM, methylated=True),\n",
       " 'tb_model': TB_Model(ELM, (2, 3)),\n",
       " 'tb_basis': ['(0, 0)', '(0, 1)', '(0, 2)', '(1, 0)', '(1, 1)', '(1, 2)'],\n",
       " 'tb_sites_flattened': ['G', 'C', 'G', 'C', 'G', 'C'],\n",
       " 'tb_basis_sites_dict': {'(0, 0)': 'G',\n",
       "  '(0, 1)': 'C',\n",
       "  '(0, 2)': 'G',\n",
       "  '(1, 0)': 'C',\n",
       "  '(1, 1)': 'G',\n",
       "  '(1, 2)': 'C'},\n",
       " 'tb_sites': array([['G', 'C', 'G'],\n",
       "        ['C', 'G', 'C']], dtype='<U1'),\n",
       " 'description': '2P',\n",
       " '_particles': ['electron', 'hole', 'exciton'],\n",
       " '_source': 'Hawke2010',\n",
       " '_unit': 'rad/ps',\n",
       " 'tb_params_electron': {'E_A': -6684.776770665955,\n",
       "  'E_T': -7444.4104946052685,\n",
       "  'E_G': -6836.703515453818,\n",
       "  'E_C': -6532.850025878092,\n",
       "  't_AA': 24.308279166058018,\n",
       "  't_AT': 10.634872135150385,\n",
       "  't_AG': 1.519267447878626,\n",
       "  't_AC': -4.5578023436358786,\n",
       "  't_TA': -10.634872135150385,\n",
       "  't_TT': -45.578023436358784,\n",
       "  't_TG': -25.827546613936647,\n",
       "  't_TC': 33.42388385332978,\n",
       "  't_GA': 45.578023436358784,\n",
       "  't_GT': -48.616558332116036,\n",
       "  't_GG': 30.385348957572525,\n",
       "  't_GC': 65.32850025878092,\n",
       "  't_CA': -18.231209374543514,\n",
       "  't_CT': 95.71384921635345,\n",
       "  't_CG': 22.789011718179392,\n",
       "  't_CC': -71.40557005029542,\n",
       "  'h_AT': -13.673407030907635,\n",
       "  'h_GC': 24.308279166058018,\n",
       "  'h_TA': -13.673407030907635,\n",
       "  'h_CG': 24.308279166058018,\n",
       "  'r+_AA': 9.115604687271757,\n",
       "  'r+_AT': 3.038534895757252,\n",
       "  'r+_AG': 4.5578023436358786,\n",
       "  'r+_AC': -3.038534895757252,\n",
       "  'r+_TA': 3.038534895757252,\n",
       "  'r+_TT': 3.038534895757252,\n",
       "  'r+_TG': 4.5578023436358786,\n",
       "  'r+_TC': -3.038534895757252,\n",
       "  'r+_GA': 4.5578023436358786,\n",
       "  'r+_GT': 4.5578023436358786,\n",
       "  'r+_GG': -3.038534895757252,\n",
       "  'r+_GC': -4.5578023436358786,\n",
       "  'r+_CA': -3.038534895757252,\n",
       "  'r+_CT': -3.038534895757252,\n",
       "  'r+_CG': -4.5578023436358786,\n",
       "  'r+_CC': 3.038534895757252,\n",
       "  'r-_AA': 44.05875598848016,\n",
       "  'r-_AT': 4.5578023436358786,\n",
       "  'r-_AG': -9.115604687271757,\n",
       "  'r-_AC': -4.5578023436358786,\n",
       "  'r-_TA': 4.5578023436358786,\n",
       "  'r-_TT': 0.3038534895757252,\n",
       "  'r-_TG': 3.038534895757252,\n",
       "  'r-_TC': -0.3038534895757252,\n",
       "  'r-_GA': -9.115604687271757,\n",
       "  'r-_GT': 3.038534895757252,\n",
       "  'r-_GG': -7.596337239393131,\n",
       "  'r-_GC': -6.077069791514504,\n",
       "  'r-_CA': -4.5578023436358786,\n",
       "  'r-_CT': -0.3038534895757252,\n",
       "  'r-_CG': -6.077069791514504,\n",
       "  'r-_CC': 0.4557802343635879},\n",
       " 'tb_params_hole': {'E_A': -12609.919817392598,\n",
       "  'E_T': -13673.407030907636,\n",
       "  'E_G': -12154.13958302901,\n",
       "  'E_C': -13369.55354133191,\n",
       "  't_AA': -12.154139583029009,\n",
       "  't_AT': 103.31018645574659,\n",
       "  't_AG': -7.596337239393131,\n",
       "  't_AC': 103.31018645574659,\n",
       "  't_TA': 39.50095364484428,\n",
       "  't_TT': -177.75429140179926,\n",
       "  't_TG': 42.53948854060154,\n",
       "  't_TC': -130.65700051756184,\n",
       "  't_GA': -120.02212838241147,\n",
       "  't_GT': 110.90652369513971,\n",
       "  't_GG': -94.19458176847482,\n",
       "  't_GC': 121.5413958302901,\n",
       "  't_CA': 7.596337239393131,\n",
       "  't_CT': -162.56161692301302,\n",
       "  't_CG': -1.519267447878626,\n",
       "  't_CC': -100.27165155998934,\n",
       "  'h_AT': -18.231209374543514,\n",
       "  'h_GC': -18.231209374543514,\n",
       "  'h_TA': -18.231209374543514,\n",
       "  'h_CG': -18.231209374543514,\n",
       "  'r+_AA': 3.038534895757252,\n",
       "  'r+_AT': 13.673407030907635,\n",
       "  'r+_AG': 6.077069791514504,\n",
       "  'r+_AC': 7.596337239393131,\n",
       "  'r+_TA': 13.673407030907635,\n",
       "  'r+_TT': 6.077069791514504,\n",
       "  'r+_TG': 7.596337239393131,\n",
       "  'r+_TC': 3.038534895757252,\n",
       "  'r+_GA': 6.077069791514504,\n",
       "  'r+_GT': 7.596337239393131,\n",
       "  'r+_GG': 4.5578023436358786,\n",
       "  'r+_GC': 6.077069791514504,\n",
       "  'r+_CA': 7.596337239393131,\n",
       "  'r+_CT': 3.038534895757252,\n",
       "  'r+_CG': 6.077069791514504,\n",
       "  'r+_CC': 1.519267447878626,\n",
       "  'r-_AA': 72.92483749817406,\n",
       "  'r-_AT': -4.5578023436358786,\n",
       "  'r-_AG': -4.5578023436358786,\n",
       "  'r-_AC': -7.596337239393131,\n",
       "  'r-_TA': -4.5578023436358786,\n",
       "  'r-_TT': 0.759633723939313,\n",
       "  'r-_TG': 7.596337239393131,\n",
       "  'r-_TC': 0.759633723939313,\n",
       "  'r-_GA': -4.5578023436358786,\n",
       "  'r-_GT': 7.596337239393131,\n",
       "  'r-_GG': -66.84776770665955,\n",
       "  'r-_GC': 6.077069791514504,\n",
       "  'r-_CA': 7.596337239393131,\n",
       "  'r-_CT': 0.759633723939313,\n",
       "  'r-_CG': 6.077069791514504,\n",
       "  'r-_CC': 1.519267447878626},\n",
       " '_relaxation': True,\n",
       " '_interaction_param': 0.0,\n",
       " 'eh_basis': [('(0, 0)', '(0, 0)'),\n",
       "  ('(0, 0)', '(0, 1)'),\n",
       "  ('(0, 0)', '(0, 2)'),\n",
       "  ('(0, 0)', '(1, 0)'),\n",
       "  ('(0, 0)', '(1, 1)'),\n",
       "  ('(0, 0)', '(1, 2)'),\n",
       "  ('(0, 1)', '(0, 0)'),\n",
       "  ('(0, 1)', '(0, 1)'),\n",
       "  ('(0, 1)', '(0, 2)'),\n",
       "  ('(0, 1)', '(1, 0)'),\n",
       "  ('(0, 1)', '(1, 1)'),\n",
       "  ('(0, 1)', '(1, 2)'),\n",
       "  ('(0, 2)', '(0, 0)'),\n",
       "  ('(0, 2)', '(0, 1)'),\n",
       "  ('(0, 2)', '(0, 2)'),\n",
       "  ('(0, 2)', '(1, 0)'),\n",
       "  ('(0, 2)', '(1, 1)'),\n",
       "  ('(0, 2)', '(1, 2)'),\n",
       "  ('(1, 0)', '(0, 0)'),\n",
       "  ('(1, 0)', '(0, 1)'),\n",
       "  ('(1, 0)', '(0, 2)'),\n",
       "  ('(1, 0)', '(1, 0)'),\n",
       "  ('(1, 0)', '(1, 1)'),\n",
       "  ('(1, 0)', '(1, 2)'),\n",
       "  ('(1, 1)', '(0, 0)'),\n",
       "  ('(1, 1)', '(0, 1)'),\n",
       "  ('(1, 1)', '(0, 2)'),\n",
       "  ('(1, 1)', '(1, 0)'),\n",
       "  ('(1, 1)', '(1, 1)'),\n",
       "  ('(1, 1)', '(1, 2)'),\n",
       "  ('(1, 2)', '(0, 0)'),\n",
       "  ('(1, 2)', '(0, 1)'),\n",
       "  ('(1, 2)', '(0, 2)'),\n",
       "  ('(1, 2)', '(1, 0)'),\n",
       "  ('(1, 2)', '(1, 1)'),\n",
       "  ('(1, 2)', '(1, 2)')],\n",
       " '_nn_cutoff': None,\n",
       " 'matrix': array([[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "          0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "        [ 0.00000000e+00, -1.89908431e+04,  1.21541396e+02, ...,\n",
       "          0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "        [ 0.00000000e+00,  1.21541396e+02, -2.02062571e+04, ...,\n",
       "          0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "        ...,\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         -1.99024036e+04,  1.21541396e+02,  0.00000000e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "          1.21541396e+02, -1.86869896e+04, -1.51926745e+00],\n",
       "        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "          0.00000000e+00, -1.51926745e+00, -1.99024036e+04]]),\n",
       " 'matrix_dim': 37,\n",
       " 'backbone': False}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tb_ham = TB_Ham(dna_seq, **ham_kwargs)\n",
    "# print all attributes of the TB_Ham instance\n",
    "tb_ham.__vars__()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f370c974",
   "metadata": {},
   "source": [
    "Finally we can return the Hamiltonian matrix that determines the unitary evolution of the charge/ exciton dynamics on the selected DNA sequence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8e86149a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       [ 0.00000000e+00, -1.89908431e+04,  1.21541396e+02, ...,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       [ 0.00000000e+00,  1.21541396e+02, -2.02062571e+04, ...,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       ...,\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "        -1.99024036e+04,  1.21541396e+02,  0.00000000e+00],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         1.21541396e+02, -1.86869896e+04, -1.51926745e+00],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         0.00000000e+00, -1.51926745e+00, -1.99024036e+04]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tb_ham.matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae506b14",
   "metadata": {},
   "source": [
    "The TB_Ham class has an method that performs the Fourier analysis on the Hamiltonian and returns the average population, amplitude and frequency of a DNA base given a certain initial state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8a694991",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({},\n",
       " {},\n",
       " {'electron': 0.46006927979479517,\n",
       "  'hole': 0.979822728019389,\n",
       "  'exciton': 0.4507863368064506})"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initial state \n",
    "init_state = tb_model.eh_basis[0]\n",
    "# DNA base for which the Fourier components are calculated\n",
    "end_state = tb_model.tb_basis[0]\n",
    "\n",
    "# Average population of the chosen base \n",
    "tb_ham.get_fourier(init_state, end_state, ['average_pop'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7efe71ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "   ...],\n",
       "  'exciton': [4.728431918319125e-06,\n",
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       "   26.59508624060618,\n",
       "   21.441425918936147]},\n",
       " {})"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Amplitudes and Frequencies on the chosen base \n",
    "tb_ham.get_fourier(init_state, end_state, ['amplitude', 'frequency'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dd70113",
   "metadata": {},
   "source": [
    "It is easier to visualize the amplitudes and frequencies of the Fourier decomposition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "90a0f3bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from qDNA.plotting import plot_fourier\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plot_fourier(ax, tb_ham, init_state, end_state, 'Period')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f5c0e07",
   "metadata": {},
   "source": [
    "# Custom tight-binding model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d80cf282-3656-4241-9320-c670383ead73",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qDNA.model import Custom_TB_Model, save_tb_params, load_tb_params, tb_ham_1P"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a83781",
   "metadata": {},
   "source": [
    "1. Create a tight-binding model describing hierarchical relations between persons (tree-shaped)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7933288a-9e32-4048-bcf4-0184eb5f9ff6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# input \n",
    "tb_model_name = 'my_model'\n",
    "num_strands = 1\n",
    "tb_basis = ['P0', 'P1', 'P2', 'P3']\n",
    "tb_config = [('relation', 'P0', 'P1'),\n",
    "             ('relation', 'P0', 'P2'), \n",
    "             ('relation', 'P0', 'P3')]\n",
    "\n",
    "tb_dims = ( num_strands, len(tb_basis)//num_strands )\n",
    "tb_model = Custom_TB_Model(tb_model_name, tb_dims, tb_basis, tb_config)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47a95038",
   "metadata": {},
   "source": [
    "2. Specify the persons and rate their relations with a number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "107bef50",
   "metadata": {},
   "outputs": [],
   "source": [
    "tb_sites = ['Alice', 'Bob', 'Charlie', 'Eve']\n",
    "tb_param_dict = {'relation_AliceBob': 5, 'relation_AliceCharlie': 3, 'relation_AliceEve': -2,\n",
    "            'relation_BobAlice': 5, 'relation_CharlieAlice': 3, 'relation_EveAlice': -2}\n",
    "info_dict={'author': 'Herb2024', 'subject': 'relations_between_persons'}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9d98986",
   "metadata": {},
   "source": [
    "3. Save and load the created dictionary to be able to reuse and look up the parameters later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "12c1d5bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "directory = os.path.join(ROOT_DIR, \"qDNA\", \"data\", \"raw\", \"test_params\")\n",
    "save_tb_params(tb_param_dict, info_dict, directory = directory, notes = 'The parameters describe relations between persons.')\n",
    "tb_param_dict = load_tb_params(info_dict, directory = directory, load_metadata = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02b2c5ff",
   "metadata": {},
   "source": [
    "4. Create the corresponding matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "188608b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  5.,  3., -2.],\n",
       "       [ 5.,  0.,  0.,  0.],\n",
       "       [ 3.,  0.,  0.,  0.],\n",
       "       [-2.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tb_ham_matrix = tb_ham_1P(tb_model, tb_param_dict, dict(zip(tb_basis, tb_sites)) )\n",
    "tb_ham_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cf2c49a",
   "metadata": {},
   "source": [
    "# Analysis of the custom tight-binding model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "dabfb700-29d1-437a-8aed-cfa5221963c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from qDNA.tools import save_figure\n",
    "from qDNA.utils import calc_average_pop, calc_amplitudes, calc_frequencies, get_pop_fourier\n",
    "from qDNA.plotting import get_frame_fourier"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c77ac495",
   "metadata": {},
   "source": [
    "As an example we plot the Fourier analysis of the Hamiltonian. As expected there is one dominant timescale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a4a508f4-6523-4123-9c8d-b21a04e144dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average population: 0.4999999999999998\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eigv, eigs = np.linalg.eigh(tb_ham_matrix)\n",
    "amplitudes = calc_amplitudes(eigs, 0, 0)\n",
    "frequencies = calc_frequencies(eigv)\n",
    "average_pop = calc_average_pop(eigs, 0, 0)\n",
    "fig, ax = plt.subplots()\n",
    "get_frame_fourier(ax, x_axis='frequencies')\n",
    "ax.plot(frequencies, amplitudes, '.', markersize = 15)\n",
    "save_figure(fig, 'test_fourier', os.path.join(ROOT_DIR, \"qDNA\", \"data\", \"figures\", \"test_plots\"), format='pdf')\n",
    "print(f'Average population: {average_pop}')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "663d8c62",
   "metadata": {},
   "source": [
    "Plot of the population dynamics for Alice interacting with her colleagues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2e5595b3-bea7-45b5-9176-64411f0ed88f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The vertical line is calculated as $2*np.pi/frequency$\n",
    "\n",
    "times = np.linspace(0,1,100)\n",
    "pop_list = [get_pop_fourier(t, average_pop, amplitudes, frequencies) for t in times]\n",
    "plt.plot(times, pop_list)\n",
    "plt.axvline(x=0.5096)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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