time_propagator,
t[-1],
time_step,
wave_nums=False)
return dynamics[:, 0]
print '[Calculating Forster rates...]'
print 'Started at: ' + str(time_utils.getTime())
for i, v in enumerate(reorg_energy_values):
#print 'Calculating rates for reorg energy: ' + str(v)
forster_time = np.linspace(0, 20., 16000)
lbf = os.site_lbf_ed(forster_time,
os.lbf_coeffs(v, cutoff_freq, temperature, None, 5))
forster_rates[i] = os.forster_rate(100., 0, v, v, lbf, lbf, 0, 0,
np.array([1., 0]), np.array([0, 1.]),
system_hamiltonian, forster_time)
print 'Finished at: ' + str(time_utils.getTime())
def calculate_HEOM(reorg_energy):
print reorg_energy
system_hamiltonian = np.array([[100., 20.], [20., 0]])
cutoff_freq = 53.
temperature = 300.
hs = HierarchySolver(system_hamiltonian,
environment(reorg_energy, beta, K),
beta,
N=trunc_level)
hs.init_system_dm = init_state
HEOM_history, time = hs.calculate_time_evolution(time_step, duration)
bare_chl_energy = system_hamiltonian[4,4] - total_reorg_energy
bare_phe_energy = system_hamiltonian[6,6] - total_reorg_energy
bare_CT1_energy = average_site_CT_energies[6] - total_reorg_energy*CT1_scaling
bare_CT2_energy = average_site_CT_energies[7] - total_reorg_energy*CT2_scaling
chl_state = np.array([0, 0, 1., 0, 0, 0, 0, 0])
phe_state = np.array([0, 0, 0, 0, 1., 0, 0, 0])
CT1_state = np.array([0, 0, 0, 0, 0, 0, 1., 0])
CT2_state = np.array([0, 0, 0, 0, 0, 0, 0, 1.])
time = np.linspace(0,2.,256000)
site_lbf = os.site_lbf_ed(time, os.lbf_coeffs(reorg_energy, cutoff_freq, temperature, None, 100))
# primary CT rates in site basis
chl_CT1_rate = os.forster_rate(bare_chl_energy, bare_CT1_energy, reorg_energy, reorg_energy*CT1_scaling, \
site_lbf, site_lbf*CT1_scaling, 0, 0, chl_state, CT1_state, coherent_hamiltonian, time)
CT1_chl_rate = os.forster_rate(bare_CT1_energy, bare_chl_energy, reorg_energy, reorg_energy*CT1_scaling, \
site_lbf, site_lbf*CT1_scaling, 0, 0, chl_state, CT1_state, coherent_hamiltonian, time)
phe_CT1_rate = os.forster_rate(bare_phe_energy, bare_CT1_energy, reorg_energy, reorg_energy*CT1_scaling, \
site_lbf, site_lbf*CT1_scaling, 0, 0, phe_state, CT1_state, coherent_hamiltonian, time)
CT1_phe_rate = os.forster_rate(bare_CT1_energy, bare_phe_energy, reorg_energy, reorg_energy*CT1_scaling, \
site_lbf, site_lbf*CT1_scaling, 0, 0, phe_state, CT1_state, coherent_hamiltonian, time)
forward_exciton_CT_rates = [2.86359127e+00, 2.09614196e-02, 7.89708095e+01, 5.47195323e+00, 2.91393623e+00, 2.92997893e-01]
backward_exciton_CT_rates = [2.32445332e+00, 1.40848357e-02, 4.18754762e+01, 2.46325661e+00, 1.25847348e+00, 3.69904601e-02]
# secondary CT rates
CT1_CT2_rate = os.forster_rate(bare_CT1_energy, bare_CT2_energy, reorg_energy*CT1_scaling, reorg_energy*CT2_scaling, \
site_lbf*CT1_scaling, site_lbf*CT2_scaling, 0, 0, CT1_state, CT2_state, coherent_hamiltonian, time)
CT2_CT1_rate = os.forster_rate(bare_CT2_energy, bare_CT1_energy, reorg_energy*CT1_scaling, reorg_energy*CT2_scaling, \
site_lbf*CT1_scaling, site_lbf*CT2_scaling, 0, 0, CT1_state, CT2_state, coherent_hamiltonian, time)
init_state = np.array([[1., 0], [0, 0]])
hs = HierarchySolver(system_hamiltonian, 1., cutoff_freq, temperature)
# error function for least squares fit
def residuals(p, y, pops1, pops2):
k12, k21 = p
return y - (-k12*pops1 + k21*pops2)
print '[Calculating Forster rates...]'
print 'Started at: ' + str(time_utils.getTime())
for i,v in enumerate(reorg_energy_values):
#print 'Calculating rates for reorg energy: ' + str(v)
forster_time = np.linspace(0, 20., 16000)
lbf = os.site_lbf_ed(forster_time, os.lbf_coeffs(v, cutoff_freq, temperature, None, 5))
forster_rates[i] = os.forster_rate(100., 0, v, v, lbf, lbf, 0, 0, np.array([1., 0]), np.array([0, 1.]), system_hamiltonian, forster_time)
print 'Finished at: ' + str(time_utils.getTime())
def calculate_HEOM(reorg_energy):
system_hamiltonian = np.array([[100., 20.], [20., 0]])
cutoff_freq = 53.
temperature = 300.
init_state = np.array([[1., 0], [0, 0]])
time_step = 0.00005
duration = 5.
hs = HierarchySolver(system_hamiltonian, reorg_energy, cutoff_freq, temperature)
HEOM_history, time = hs.hierarchy_time_evolution(init_state, 18, time_step, duration)
return HEOM_history
# lbf = site_lbf[i]
# break
# return np.exp(1.j*(E1-E2)*t) * np.exp(-1.j*(E_reorg1+E_reorg2)*t) * np.exp(-lbf-lbf)
#
# print 2. * integrate.simps(np.real(np.array([integrand_func(t) for t in time])))
#
# plt.plot(time, np.array([integrand_func(t) for t in time]))
# plt.show()
# try to reproduce dimer rates using code copied from Mathematica
rates_data = []
time_interval = 20
time = np.linspace(0, time_interval, time_interval*16000)
site_lbf = os.site_lbf_ed(time, os.lbf_coeffs(reorg_energy, cutoff_freq, temperature, None, 20))
for i,V in enumerate(coupling_values):
rates = []
for delta_E in delta_E_values:
H = hamiltonian(delta_E, V)
rates.append(os.forster_rate(H[0,0], H[1,1], reorg_energy, reorg_energy, site_lbf, site_lbf, 0, 0, np.array([1.,0]), np.array([0,1.]), H, time))
rates_data.append(rates)
for i,rates in enumerate(rates_data):
plt.subplot(1,3,i+1)
plt.loglog(delta_E_values, utils.WAVENUMS_TO_INVERSE_PS*np.array(rates))
plt.ylim(0.01, 200)
plt.xlim(5,1000)
plt.show()
primary_CT_scaling = 3.
primary_CT_reorg_energy = primary_CT_scaling * total_site_reorg_energy
primary_CT_state = np.array([0, 0, 0, 0, 0, 0, 1., 0])
secondary_CT_scaling = 4.
secondary_CT_reorg_energy = secondary_CT_scaling * total_site_reorg_energy
secondary_CT_state = np.array([0, 0, 0, 0, 0, 0, 0, 1.])
# calculate Forster rates to primary and secondary CT states
forward_primary_forster_rates = np.zeros(site_hamiltonian.shape[0])
backward_primary_forster_rates = np.zeros(site_hamiltonian.shape[0])
for i,E in enumerate(evals):
# double check the effect of the lifetimes on the Forster rates
# also check Forster rates converge with the number of time points used
forward_primary_forster_rates[i] = os.forster_rate(E, hamiltonian[6,6]-primary_CT_reorg_energy, exciton_reorg_energies[i], primary_CT_reorg_energy, \
exciton_lbfs[i], primary_CT_scaling*lbf, 0, 0, \
np.append(evecs[i], [0,0]), primary_CT_state, hamiltonian, time)
backward_primary_forster_rates[i] = os.forster_rate(hamiltonian[6,6]-primary_CT_reorg_energy, E, exciton_reorg_energies[i], primary_CT_reorg_energy, \
exciton_lbfs[i], primary_CT_scaling*lbf, 0, 0, \
np.append(evecs[i], [0,0]), primary_CT_state, hamiltonian, time)
# construct Liouvillian
liouvillian = np.zeros(hamiltonian.shape)
liouvillian[:6,:6] = MRT_rates
liouvillian[6,:6] = forward_primary_forster_rates
liouvillian.T[6,:6] = backward_primary_forster_rates
# forward secondary CT rate
liouvillian[7,6] = os.forster_rate(hamiltonian[6,6]-primary_CT_reorg_energy, hamiltonian[7,7]-secondary_CT_reorg_energy, \
primary_CT_reorg_energy, secondary_CT_reorg_energy, \
primary_CT_scaling*lbf, secondary_CT_scaling*lbf, 0, 0, \
primary_CT_state, secondary_CT_state, hamiltonian, time)