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quantshah/heom_example.ipynb

Created January 11, 2018 08:04
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General HEOM code for sum of exponentials
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heom_example.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# General heirarchy model/method"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"from qutip.models.heirarchy import Heirarchy\n",
"from qutip import sigmaz, sigmax, basis, Qobj\n",
"from qutip.solver import Options\n",
"import numpy as np\n",
"\n",
"from math import pi\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exponentials"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ckAR=[-0.0531994+0.359753j, -(0.0531994+0.359753j),(0.265019-0.737435j), (0.265019+0.737435j)]\n",
"\n",
"vkAR=[-2.02381-3.37591j,-2.02381+3.37591j,-1.90802-1.16867j,-1.90802+1.16867j]\n",
"vkAR=[-vk for vk in vkAR] \n",
"\n",
"ckAI=[0.0571124-0.0269892j, 0.0571124+0.0269892j,-0.0573738+0.00965229j, -(0.0573738+0.00965229j)] \n",
"vkAI=[-1.70538-3.55923j,-1.70538+3.55923j,-1.40539-1.46163j,-1.40539+1.46163j]\n",
"vkAI=[-vk for vk in vkAI]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# System specifications"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"NR=2\n",
"NI=2\n",
"\n",
"Q = sigmaz()\n",
"Del =np.pi/2. \n",
"wq= 0.0 # Energy of the 2-level system.\n",
"Hsys = 0.5 * wq * sigmaz() + 0.5 * Del * sigmax()\n",
"\n",
"wc = 0.05 # Cutoff frequency.\n",
"alpha = 0.1/pi # Coupling strength.\n",
"N = 15 # Number of cavity fock states.\n",
"Temperature = 1/0.95 # Tempertaure.\n",
"tlist = np.linspace(0, 1, 100)\n",
"\n",
"#for amirs Omega= pi data, tlist is different (actually a bit weird)\n",
"#tlist=tlistA\n",
"\n",
"initial_state = basis(2,1) * basis(2,1).dag() # Initial state of the system.\n",
"#return_vals = [tensor(qeye(N), kk) for kk in [Q]] # List for which to calculate expectation value\n",
"return_vals = [initial_state, basis(2,0) * basis(2,1).dag() ] # List for which to calculate expectation value\n",
"eigen_sparse = False\n",
"calc_time = True \n",
"options = Options(nsteps=15000, store_states=True,rtol=1e-17, atol=1e-17) # Options for the solver.\n",
"\n",
"#Convergence parameters\n",
"#Nc is the cut-off, and depends on Nc>> \n",
"Nc = 3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Invoking the model and the solver"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"model = Heirarchy(hamiltonian=Hsys, coupling=Q, Nc=Nc,\n",
" real_prefactors= ckAR, real_exponents=vkAR,\n",
" complex_prefactors=ckAI, complex_exponents=vkAI)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"liouv = Qobj(model.liouvillian())"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[660], [660]], shape = (660, 660), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -0.785j & 0.785j & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-0.785j & 0.0 & 0.0 & 0.785j & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.785j & 0.0 & 0.0 & -0.785j & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.785j & -0.785j & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\(-0.476-0.080j) & 0.0 & 0.0 & 0.0 & (-1.405+1.462j) & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & (-6.071-3.376j) & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & (-6.071-10.128j) & -0.785j & 0.785j & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & -0.785j & (-6.071-10.128j) & 0.0 & 0.785j\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.785j & 0.0 & (-6.071-10.128j) & -0.785j\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.785j & -0.785j & (-6.071-10.128j)\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[660], [660]], shape = (660, 660), type = oper, isherm = False\n",
"Qobj data =\n",
"[[ 0.00000 +0.j 0.00000 -0.78539816j 0.00000 +0.78539816j ...,\n",
" 0.00000 +0.j 0.00000 +0.j 0.00000 +0.j ]\n",
" [ 0.00000 -0.78539816j 0.00000 +0.j 0.00000 +0.j ...,\n",
" 0.00000 +0.j 0.00000 +0.j 0.00000 +0.j ]\n",
" [ 0.00000 +0.78539816j 0.00000 +0.j 0.00000 +0.j ...,\n",
" 0.00000 +0.j 0.00000 +0.j 0.00000 +0.j ]\n",
" ..., \n",
" [ 0.00000 +0.j 0.00000 +0.j 0.00000 +0.j ...,\n",
" -6.07143-10.12773j 0.00000 +0.j 0.00000 +0.78539816j]\n",
" [ 0.00000 +0.j 0.00000 +0.j 0.00000 +0.j ...,\n",
" 0.00000 +0.j -6.07143-10.12773j 0.00000 -0.78539816j]\n",
" [ 0.00000 +0.j 0.00000 +0.j 0.00000 +0.j ...,\n",
" 0.00000 +0.78539816j 0.00000 -0.78539816j -6.07143-10.12773j ]]"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"liouv"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"result = model.solve(initial_state, tlist, options=options)"
]
},
{
"cell_type": "code",
"execution_count": null,
"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": "3.6.2"
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"nbformat": 4,
"nbformat_minor": 2
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