def test_propagation_in_different_basis(self):
"""(LINDBLAD) Testing comparison of propagations in different bases
"""
LT1 = LindbladForm(self.H1, self.sbi1, as_operators=True)
LT2 = LindbladForm(self.H1, self.sbi1, as_operators=False)
time = TimeAxis(0.0, 1000, 1.0)
prop1 = ReducedDensityMatrixPropagator(time, self.H1, LT1)
prop2 = ReducedDensityMatrixPropagator(time, self.H1, LT2)
rho0 = ReducedDensityMatrix(dim=self.H1.dim)
rho0.data[1, 1] = 1.0
with eigenbasis_of(self.H1):
rhot1_e = prop1.propagate(rho0)
with eigenbasis_of(self.H1):
rhot2_e = prop2.propagate(rho0)
rhot1_l = prop1.propagate(rho0)
rhot2_l = prop2.propagate(rho0)
numpy.testing.assert_allclose(rhot1_l.data, rhot1_e.data)
numpy.testing.assert_allclose(rhot2_l.data, rhot2_e.data)
numpy.testing.assert_allclose(rhot1_e.data,
rhot2_e.data) #, rtol=1.0e-2)
def test_transformation_in_different_basis(self):
"""(LINDBLAD) Testing transformations into different bases
"""
#Manager().warn_about_basis_change = True
#Manager().warn_about_basis_changing_objects = True
LT1 = LindbladForm(self.H1, self.sbi1, as_operators=True, name="LT1")
LT2 = LindbladForm(self.H1, self.sbi1, as_operators=False, name="LT2")
rho0 = ReducedDensityMatrix(dim=self.H1.dim, name="ahoj")
with eigenbasis_of(self.H1):
rho0.data[1, 1] = 0.7
rho0.data[0, 0] = 0.3
with eigenbasis_of(self.H1):
rhot1_e = LT1.apply(rho0, copy=True)
with eigenbasis_of(self.H1):
rhot2_e = LT2.apply(rho0, copy=True)
rhot1_l = LT1.apply(rho0, copy=True)
rhot2_l = LT2.apply(rho0, copy=True)
numpy.testing.assert_allclose(rhot1_l.data, rhot1_e.data)
numpy.testing.assert_allclose(rhot2_l.data, rhot2_e.data)
numpy.testing.assert_allclose(rhot1_e.data,
rhot2_e.data) #, rtol=1.0e-2)
def test_comparison_of_rates(self):
"""Testing that Lindblad tensor and rate matrix are compatible
"""
tensor = True
# matrix = True
dim = self.H1.dim
KT = numpy.zeros((dim, dim), dtype=numpy.float64)
KM = numpy.zeros((dim, dim), dtype=numpy.float64)
if tensor:
#print(self.H1)
LT = LindbladForm(self.H1, self.sbi1, as_operators=False)
for n in range(2):
for m in range(2):
#print(n,m,numpy.real(RT.data[n,n,m,m]))
KT[n, m] = numpy.real(LT.data[n, n, m, m])
KM = numpy.zeros((dim, dim))
KM[0, 0] = -self.rates[1]
KM[1, 1] = -self.rates[0]
KM[0, 1] = self.rates[0]
KM[1, 0] = self.rates[1]
numpy.testing.assert_allclose(KT, KM, rtol=1.0e-2)
def test_comparison_of_dynamics(self):
"""Testing site basis dynamics by Lindblad
"""
LT1 = LindbladForm(self.H1, self.sbi1, as_operators=True)
LT2 = LindbladForm(self.H1, self.sbi1, as_operators=False)
time = TimeAxis(0.0, 1000, 1.0)
prop1 = ReducedDensityMatrixPropagator(time, self.H1, LT1)
prop2 = ReducedDensityMatrixPropagator(time, self.H1, LT2)
rho0 = ReducedDensityMatrix(dim=self.H1.dim)
rho0.data[1, 1] = 1.0
rhot1 = prop1.propagate(rho0)
rhot2 = prop2.propagate(rho0)
numpy.testing.assert_allclose(rhot1.data, rhot2.data) #, rtol=1.0e-2)
def test_transformation_in_different_basis(self):
"""(LINDBLAD) Testing transformations into different bases
"""
#Manager().warn_about_basis_change = True
#Manager().warn_about_basis_changing_objects = True
LT1 = LindbladForm(self.H1, self.sbi1, as_operators=True, name="LT1")
LT2 = LindbladForm(self.H1, self.sbi1, as_operators=False, name="LT2")
rho0 = ReducedDensityMatrix(dim=self.H1.dim, name="ahoj")
with eigenbasis_of(self.H1):
rho0.data[1,1] = 0.7
rho0.data[0,0] = 0.3
with eigenbasis_of(self.H1):
rhot1_e = LT1.apply(rho0, copy=True)
with eigenbasis_of(self.H1):
rhot2_e = LT2.apply(rho0, copy=True)
rhot1_l = LT1.apply(rho0, copy=True)
rhot2_l = LT2.apply(rho0, copy=True)
numpy.testing.assert_allclose(rhot1_l.data, rhot1_e.data)
numpy.testing.assert_allclose(rhot2_l.data, rhot2_e.data)
numpy.testing.assert_allclose(rhot1_e.data, rhot2_e.data) #, rtol=1.0e-2)
K.data[1, 2] = 1.0
#
# System bath interaction with prescribed rate
#
from quantarhei.qm import SystemBathInteraction
sbi = SystemBathInteraction(sys_operators=[K], rates=(1.0 / 100, ))
agg.set_SystemBathInteraction(sbi)
#
# Corresponding Lindblad form
#
from quantarhei.qm import LindbladForm
LF = LindbladForm(HH, sbi, as_operators=False)
print(LF.data[1, 1, 2, 2])
print(LF.data[1, 2, 1, 2])
#
# We can get it also from the aggregate
#
from quantarhei import TimeAxis
time = TimeAxis()
# time is not used here at all
LFa, ham = agg.get_RelaxationTensor(time,
relaxation_theory="electronic_Lindblad")
def test_comparison_of_exciton_dynamics(self):
"""Testing exciton basis dynamics by Lindblad
"""
# site basis form to be compared with
LT1 = LindbladForm(self.H1, self.sbi1, as_operators=True)
# exciton basis forms
LT13 = LindbladForm(self.H3, self.sbi3, as_operators=True)
LT23 = LindbladForm(self.H3, self.sbi3, as_operators=False)
LT4e = LindbladForm(self.H4, self.sbi4e, as_operators=True)
LT4s = LindbladForm(self.H4s, self.sbi4s, as_operators=True)
time = TimeAxis(0.0, 1000, 1.0)
#
# Propagators
#
prop0 = ReducedDensityMatrixPropagator(time, self.H1, LT1)
prop1 = ReducedDensityMatrixPropagator(time, self.H3, LT13)
prop2 = ReducedDensityMatrixPropagator(time, self.H3, LT23)
prop4e = ReducedDensityMatrixPropagator(time, self.H4, LT4e)
prop4s = ReducedDensityMatrixPropagator(time, self.H4s, LT4s)
#
# Initial conditions
#
rho0 = ReducedDensityMatrix(dim=self.H3.dim)
rho0c = ReducedDensityMatrix(dim=self.H1.dim) # excitonic
with eigenbasis_of(self.H3):
rho0c.data[1, 1] = 1.0
rho0.data[1, 1] = 1.0
rho04e = ReducedDensityMatrix(dim=self.H4.dim)
rho04s = ReducedDensityMatrix(dim=self.H4.dim)
with eigenbasis_of(self.H4):
rho04e.data[2, 2] = 1.0
rho04s.data[2, 2] = 1.0
#
# Propagations
#
rhotc = prop0.propagate(rho0c)
rhot1 = prop1.propagate(rho0)
rhot2 = prop2.propagate(rho0)
rhot4e = prop4e.propagate(rho04e)
rhot4s = prop4s.propagate(rho04s)
# propagation with operator- and tensor forms should be the same
numpy.testing.assert_allclose(rhot1.data, rhot2.data) #, rtol=1.0e-2)
#
# Population time evolution by Lindblad is independent
# of the level structure and basis, as long as I compare
# populations in basis in which the Lindblad form was defined
#
P = numpy.zeros((2, time.length))
Pc = numpy.zeros((2, time.length))
P4e = numpy.zeros((3, time.length))
P4s = numpy.zeros((3, time.length))
with eigenbasis_of(self.H3):
for i in range(time.length):
P[0, i] = numpy.real(rhot1.data[i, 0,
0]) # population of exciton 0
P[1, i] = numpy.real(rhot1.data[i, 1,
1]) # population of exciton 1
for i in range(time.length):
Pc[0, i] = numpy.real(rhotc.data[i, 0,
0]) # population of exciton 0
Pc[1, i] = numpy.real(rhotc.data[i, 1,
1]) # population of exciton 1
# we compare populations
numpy.testing.assert_allclose(Pc, P) #, rtol=1.0e-2)
with eigenbasis_of(self.H4):
for i in range(time.length):
P4e[0,
i] = numpy.real(rhot4e.data[i, 0,
0]) # population of exciton 0
P4e[1,
i] = numpy.real(rhot4e.data[i, 1,
1]) # population of exciton 1
P4e[2,
i] = numpy.real(rhot4e.data[i, 2,
2]) # population of exciton 1
for i in range(time.length):
P4s[0, i] = numpy.real(rhot4s.data[i, 0,
0]) # population of exciton 0
P4s[1, i] = numpy.real(rhot4s.data[i, 1,
1]) # population of exciton 1
P4s[2, i] = numpy.real(rhot4s.data[i, 2,
2]) # population of exciton 1
# import matplotlib.pyplot as plt
#
# plt.plot(time.data,P4s[0,:], "-r")
# plt.plot(time.data,P4s[1,:], "-r")
# plt.plot(time.data,P4s[2,:], "-r")
# plt.plot(time.data,P4e[0,:], "-g")
# plt.plot(time.data,P4e[1,:], "-g")
# plt.plot(time.data,P4e[2,:], "-g")
# plt.show()
numpy.testing.assert_allclose(P4e, P4s, atol=1.0e-8)
def test_Lindblad_dynamics_comp(self):
"""Compares Lindblad dynamics calculated from propagator and superoperator
"""
# Aggregate
import quantarhei as qr
import quantarhei.models.modelgenerator as mgen
time = qr.TimeAxis(0.0, 1000, 1.0)
# create a model
mg = mgen.ModelGenerator()
agg = mg.get_Aggregate(name="trimer-1")
agg.build()
ham = agg.get_Hamiltonian()
# calculate relaxation tensor
with qr.eigenbasis_of(ham):
#
# Operator describing relaxation
#
from quantarhei.qm import Operator
K = Operator(dim=ham.dim, real=True)
K.data[1, 2] = 1.0
#
# System bath interaction with prescribed rate
#
from quantarhei.qm import SystemBathInteraction
sbi = SystemBathInteraction(sys_operators=[K],
rates=(1.0 / 100.0, ))
agg.set_SystemBathInteraction(sbi)
#
# Corresponding Lindblad form
#
from quantarhei.qm import LindbladForm
LF = LindbladForm(ham, sbi, as_operators=False)
#
# Evolution of reduced density matrix
#
prop = qr.ReducedDensityMatrixPropagator(time, ham, LF)
#
# Evolution by superoperator
#
eSO = qr.qm.EvolutionSuperOperator(time, ham, LF)
eSO.set_dense_dt(5)
eSO.calculate()
# compare the two propagations
pairs = [(1, 3), (3, 2), (3, 3)]
for p in pairs:
rho_i1 = qr.ReducedDensityMatrix(dim=ham.dim)
rho_i1.data[p[0], p[1]] = 1.0
rho_t1 = prop.propagate(rho_i1)
exp_rho_t2 = eSO.data[:, :, :, p[0], p[1]]
#import matplotlib.pyplot as plt
#plt.plot(rho_t1.TimeAxis.data, numpy.real(rho_t1.data[:,p[0],p[1]]))
#plt.plot(rho_t1.TimeAxis.data, numpy.real(exp_rho_t2[:,p[0],p[1]]))
#plt.show()
#numpy.testing.assert_allclose(RRT.data, rtd)
numpy.testing.assert_allclose(numpy.real(rho_t1.data[:, :, :]),
numpy.real(exp_rho_t2[:, :, :]),
rtol=1.0e-7,
atol=1.0e-6)