time_propagator[1, 0] = k01
time_step = t[1] - t[0]
dynamics = te.liouvillian_time_evolution(np.array([1, 0]),
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)
e1 = 1000.0
delta_E_values = np.logspace(0, 3.0, 100) # wavenumbers
coupling_values = np.array([20.0, 100.0, 500.0]) # wavenumbers
def hamiltonian(delta_E, V):
return np.array([[delta_E / 2.0, V], [V, -delta_E / 2.0]])
reorg_energy = 100.0 # wavenumbers
cutoff_freq = 53.0 # wavenumbers
temperature = 300.0
time = np.linspace(0, 0.5, 1000)
lbf_coeffs = os.lbf_coeffs(reorg_energy, cutoff_freq, temperature, None, 0)
site_lbf = os.site_lbf_ed(time, lbf_coeffs)
site_lbf_dot = os.site_lbf_dot_ed(time, lbf_coeffs)
site_lbf_dot_dot = os.site_lbf_dot_dot_ed(time, lbf_coeffs)
"""
# comparison of reorganisation energy calculations
exciton_reorg_energies1 = []
exciton_reorg_energies2 = []
for i,delta_E in enumerate(delta_E_values):
evals, evecs = utils.sorted_eig(hamiltonian(delta_E, 20.))
exciton_reorg_energies1.append(os.generalised_exciton_reorg_energy(np.array([evecs[0], evecs[0], evecs[1], evecs[1]]), np.array([reorg_energy, reorg_energy])))
exciton_reorg_energies2.append(np.sum(evecs[0]**2 * evecs[1]**2) * reorg_energy)
plt.plot(delta_E_values, exciton_reorg_energies1, label='1')
plt.plot(delta_E_values, exciton_reorg_energies2, label='2', linewidth=2, ls='--', color='red')
plt.legend()
reorg_energy = 100. # wavenumbers
cutoff_freq = 53. # wavenumbers
temperature = 300.
# rates, integrands, time = os.MRT_rate_ed(hamiltonian(10.,500.), reorg_energy, cutoff_freq, temperature, None, 0, 60.0)
# plt.plot(time, integrands[0,1])
# plt.show()
# try to reproduce dimer rates using code copied from Mathematica
rates_data = []
time_interval = 0.5
time = np.linspace(0, time_interval, int(time_interval * 2000))
lbf_coeffs = os.lbf_coeffs(reorg_energy, cutoff_freq, temperature, None, 0)
g_site = os.site_lbf_ed(time, lbf_coeffs)
g_site_dot = os.site_lbf_dot_ed(time, lbf_coeffs)
g_site_dot_dot = os.site_lbf_dot_dot_ed(time, lbf_coeffs)
scaling = 1.
for i, V in enumerate(coupling_values):
print 'calculating rates for coupling ' + str(V)
rates = []
for delta_E in delta_E_values:
evals, evecs = utils.sorted_eig(hamiltonian(delta_E, V))
print evals
exciton_reorg_energies = np.array([
os.exciton_reorg_energy(exciton, [reorg_energy, reorg_energy])
for exciton in evecs
])
print exciton_reorg_energies
total_reorg_energy = 540.
CT1_scaling = 3.
CT2_scaling = 4.
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
try:
data = np.load(data_filename)
print 'data file already exists, do you want to append to it?'
except:
pass
time_interval = 10
integration_time = np.linspace(0, time_interval, time_interval*16000) # time_interval*16000
num_expansion_terms = 10
mode_params = PE545_mode_params(mode_damping)
coeffs = os.lbf_coeffs(reorg_energy1, cutoff_freq1, temperature, mode_params, num_expansion_terms)
coeffs = np.concatenate((coeffs, os.lbf_coeffs(reorg_energy2, cutoff_freq2, temperature, None, num_expansion_terms)))
g_site = os.site_lbf_ed(integration_time, coeffs)
g_site_dot = os.site_lbf_dot_ed(integration_time, coeffs)
g_site_dot_dot = os.site_lbf_dot_dot_ed(integration_time, coeffs)
total_site_reorg_energy = reorg_energy1 + reorg_energy2 + np.sum([mode[0]*mode[1] for mode in mode_params])
shift_before_diagonalisation = True
# in each realisation pick the next value from the distribution for each site to construct the Hamiltonian
for n in range(num_realisations):
print 'Calculating realisation number ' + str(n+1)
realisation_energies = np.zeros(site_energies.size)
for i in range(site_energies.size):
realisation_energies[i] = site_energy_samples[i][n]
if not shift_before_diagonalisation:
hamiltonian = np.diag(realisation_energies) + couplings + couplings.T
evals, evecs = utils.sorted_eig(hamiltonian)
site_shifts = data['site_shift']
exciton_init_states = data['D0_save_ex']
num_realisations = site_shifts.shape[0]
time_interval = 5 #10
integration_time = np.linspace(0, time_interval,
time_interval * 32000) # 16000
num_expansion_terms = 40
mode_params = PE545_mode_params(mode_damping)
coeffs = os.lbf_coeffs(reorg_energy1, cutoff_freq1, temperature, mode_params,
num_expansion_terms)
coeffs = np.concatenate(
(coeffs,
os.lbf_coeffs(reorg_energy2, cutoff_freq2, temperature, None,
num_expansion_terms)))
g_site = os.site_lbf_ed(integration_time, coeffs)
g_site_dot = os.site_lbf_dot_ed(integration_time, coeffs)
g_site_dot_dot = os.site_lbf_dot_dot_ed(integration_time, coeffs)
total_site_reorg_energy = reorg_energy1 + reorg_energy2 + np.sum(
[mode[0] * mode[1] for mode in mode_params])
# parameters for time evolution
duration = 5.
timestep = 0.01
time = np.arange(0, duration + timestep, timestep)
#init_dv = np.array([0.35, 0.12, 0.1, 0.1, 0.34, 0.61, 0.46, 0.5]) # init state in site basis
site_history_sum = np.zeros((average_site_hamiltonian.shape[0], time.size))
for n in range(num_realisations):
print 'Calculating realisation ' + str(n + 1) + ' at time ' + str(
datetime.now().time())
temperature = 300.
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