time_interval = 10
time = np.linspace(0, time_interval, 32000.*time_interval)
num_expansion_terms = 20
g_site, g_site_dot, g_site_dot_dot, total_site_reorg_energy = os.modified_redfield_params(time, site_reorg_energy, cutoff_freq, temperature, mode_params, num_expansion_terms)
total_site_reorg_energies = np.array([total_site_reorg_energy, total_site_reorg_energy])
rates_data = []
print 'Calculating rates with high energy modes....'
for V in coupling_values:
print 'Calculating rates for coupling ' + str(V)
rates = []
for i,delta_E in enumerate(delta_E_values):
site_hamiltonian = hamiltonian(delta_E, V) + np.diag(total_site_reorg_energies) # adjust site energies by reorganisation shift
evals, evecs = utils.sorted_eig(site_hamiltonian)
# calculate exciton reorganisation energies
exciton_reorg_energies = np.array([os.exciton_reorg_energy(evecs[i], total_site_reorg_energies) for i in range(site_hamiltonian.shape[0])])
print exciton_reorg_energies
evals = evals - exciton_reorg_energies # adjust to bare exciton reorganisation energies
MRT = os.modified_redfield_rates(evals, evecs, g_site, g_site_dot, g_site_dot_dot, total_site_reorg_energy, temperature, time)
rates.append(MRT[0,1])
rates_data.append(rates)
#np.savez('../../data/modified_redfield_test_high_energy_modes_data.npz', delta_E_values=delta_E_values, coupling_values=coupling_values, rates=rates_data)
for i,rates in enumerate(rates_data):
plt.subplot(1,3,i+1)
plt.plot(delta_E_values, utils.WAVENUMS_TO_INVERSE_PS*np.array(rates))
plt.show()
# data = np.load('../../data/modified_redfield_test_high_energy_modes_data.npz')
# rates = data['rates']
# delta_E_values = data['delta_E_values']
temperature, single_mode_params, 100)
lbf = os.site_lbf_ed(time, lbf_coeffs)
lbf_dot = os.site_lbf_dot_ed(time, lbf_coeffs)
lbf_dot_dot = os.site_lbf_dot_dot_ed(time, lbf_coeffs)
print 'Finished calculating lbfs at ' + str(time_utils.getTime())
np.savez(lbf_fn,
lbf=lbf,
lbf_dot=lbf_dot,
lbf_dot_dot=lbf_dot_dot,
time=time)
# calculate MRT rates
evals, evecs = utils.sorted_eig(hamiltonian[:6, :6])
exciton_reorg_energies = np.array([
os.exciton_reorg_energy(exciton, site_reorg_energies)
for exciton in evecs
])
# print evals - exciton_reorg_energies
# evals,evecs = utils.sort_evals_evecs(evals-exciton_reorg_energies, evecs)
# print evals
# MRT_rates2 = os.modified_redfield_rates_general_unordered(evals-exciton_reorg_energies, evecs, lbf, lbf_dot, lbf_dot_dot, total_site_reorg_energy, temperature, time)
#
# liouvillian2 = MRT_rates2 - np.diag(np.sum(MRT_rates2, axis=0))
#
# print evals
# print MRT_rates2
print evals - exciton_reorg_energies
#MRT_rates,evals,evecs = os.modified_redfield_rates_general(evals-exciton_reorg_energies, evecs, lbf, lbf_dot, lbf_dot_dot, total_site_reorg_energy, temperature, time)
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
rates.append(
os.modified_redfield_rates_general(
evals, evecs, np.array([g_site, scaling * g_site]),
np.array([g_site_dot, scaling * g_site_dot]),
np.array([g_site_dot_dot, scaling * g_site_dot_dot]),
np.array([reorg_energy, scaling * reorg_energy]), temperature,
time)[0][0, 1])
#rates.append(os.MRT_rates(hamiltonian(delta_E, V), np.array([reorg_energy, reorg_energy]), cutoff_freq, temperature, None)[0,1])
plt.subplot(1, coupling_values.size, i + 1)
rates_data.append(rates)
plt.loglog(delta_E_values,
np.array(rates) * utils.WAVENUMS_TO_INVERSE_PS,
[18532., 18008., 17973., 18040., 18711., 19574., 19050.,
18960.]) # no reorganisation shift included
couplings = np.array([[0, 1., -37., 37., 23., 92., -16., 12.],
[0, 0, 4., -11., 33., -39., -46., 3.],
[0, 0, 0, 45., 3., 2., -11., 34.],
[0, 0, 0, 0, -7., -17., -3., 6.],
[0, 0, 0, 0, 0, 18., 7., 6.],
[0, 0, 0, 0, 0, 0, 40., 26.], [0, 0, 0, 0, 0, 0, 0, 7.],
[0, 0, 0, 0, 0, 0, 0, 0]])
site_hamiltonian = np.diag(site_energies) + couplings + couplings.T
evals, evecs = utils.sorted_eig(site_hamiltonian)
site_reorg_shift = 110.
site_reorg_energies = np.zeros(site_energies.size)
site_reorg_energies.fill(site_reorg_shift)
shifted_site_hamiltonian = site_hamiltonian + np.diag(site_reorg_energies)
shifted_evals, shifted_evecs = utils.sorted_eig(shifted_site_hamiltonian)
exciton_reorg_energies = os.exciton_reorg_energy(shifted_evecs,
site_reorg_energies)
print evals
print shifted_evals - exciton_reorg_energies
print exciton_reorg_energies
for i, el in enumerate(evecs.flatten()):
print shifted_evecs.flatten()[i] + 0.0000001 > el > shifted_evecs.flatten(
)[i] - 0.0000001
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)
else:
hamiltonian = np.diag(realisation_energies + total_site_reorg_energy) + couplings + couplings.T # shift site energies by reorg energy
evals, evecs = utils.sorted_eig(hamiltonian) # diagonalise
site_reorg_energies = np.zeros(hamiltonian.shape[0])
site_reorg_energies.fill(total_site_reorg_energy)
exciton_reorg_energies = np.zeros(hamiltonian.shape[0])
for i in range(hamiltonian.shape[0]):
exciton_reorg_energies[i] = os.exciton_reorg_energy(evecs[i], site_reorg_energies) # calculate exciton reorg energies
evals = evals - exciton_reorg_energies # shift exciton energies down by exciton reorg energies
# calculate the rates and time evolution for the realisation
realisation_rates = os.MRT_rate_PE545_quick(evals, evecs, g_site, g_site_dot, g_site_dot_dot, total_site_reorg_energy, temperature, integration_time)
liouvillian = np.zeros((realisation_rates.shape[0], realisation_rates.shape[1]))
for i,row in enumerate(realisation_rates.T):
liouvillian[i,i] = -np.sum(row)
liouvillian += realisation_rates
# make sure to return excitons in basis going from lowest to highest energy with sorted_eig
evecs = evecs.T
init_dv = np.diag(np.dot(evecs.T, np.dot(np.diag(init_dv), evecs))) # convert init dv in site basis to exciton basis before time evolution calculation
dv_history = te.liouvillian_time_evolution(init_dv, liouvillian, duration, timestep)
temperature, mode_params(mode_damping), 100)
lbf = os.site_lbf_ed(time, lbf_coeffs)
lbf_dot = os.site_lbf_dot_ed(time, lbf_coeffs)
lbf_dot_dot = os.site_lbf_dot_dot_ed(time, lbf_coeffs)
print 'Finished calculating lbfs at ' + str(time_utils.getTime())
np.savez(lbf_fn,
lbf=lbf,
lbf_dot=lbf_dot,
lbf_dot_dot=lbf_dot_dot,
time=time)
# calculate MRT rates
evals, evecs = utils.sorted_eig(hamiltonian)
exciton_reorg_energies = np.array([
os.exciton_reorg_energy(exciton, site_reorg_energies) for exciton in evecs
])
# print evals - exciton_reorg_energies
# evals,evecs = utils.sort_evals_evecs(evals-exciton_reorg_energies, evecs)
# print evals
reorgs = np.array([total_site_reorg_energy, total_site_reorg_energy, total_site_reorg_energy,\
total_site_reorg_energy, total_site_reorg_energy, total_site_reorg_energy,\
1.5*total_site_reorg_energy])
MRT_rates2 = os.modified_redfield_rates_general_unordered(evals-exciton_reorg_energies, evecs,
np.array([lbf,lbf,lbf,lbf,lbf,lbf,1.5*lbf]), \
np.array([lbf_dot,lbf_dot,lbf_dot,lbf_dot,lbf_dot,lbf_dot,1.5*lbf_dot]), \
np.array([lbf_dot_dot,lbf_dot_dot,lbf_dot_dot,lbf_dot_dot,lbf_dot_dot,lbf_dot_dot,1.5*lbf_dot_dot]), \
reorgs,\
temperature, time)
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
rates.append(os.modified_redfield_rates_general(evals, evecs, np.array([g_site, scaling*g_site]), np.array([g_site_dot,scaling*g_site_dot]), np.array([g_site_dot_dot,scaling*g_site_dot_dot]), np.array([reorg_energy,scaling*reorg_energy]), temperature, time)[0][0,1])
#rates.append(os.MRT_rates(hamiltonian(delta_E, V), np.array([reorg_energy, reorg_energy]), cutoff_freq, temperature, None)[0,1])
plt.subplot(1, coupling_values.size, i+1)
rates_data.append(rates)
plt.loglog(delta_E_values, np.array(rates)*utils.WAVENUMS_TO_INVERSE_PS, label=V)
# plot extracted data from Ed's thesis
# xdata, ydata = np.loadtxt('../../data/thieved_data'+str(i)+'.txt', delimiter=', ', unpack=True)
# plt.loglog(xdata, ydata, color='red')
#s = interp.UnivariateSpline(xdata, ydata, k=2, s=None)
#plt.loglog(xdata, s(xdata), color='red')
plt.xlabel(r'$\Delta E$ (cm$^{-1}$)')
plt.ylabel(r'rate')
# basis { PEB_50/61C, DBV_A, DVB_B, PEB_82C, PEB_158C, PEB_50/61D, PEB_82D, PEB_158D }
site_energies = np.array([18532., 18008., 17973., 18040., 18711., 19574., 19050., 18960.]) # no reorganisation shift included
couplings = np.array([[0, 1., -37., 37., 23., 92., -16., 12.],
[0, 0, 4., -11., 33., -39., -46., 3.],
[0, 0, 0, 45., 3., 2., -11., 34.],
[0, 0, 0, 0, -7., -17., -3., 6.],
[0, 0, 0, 0, 0, 18., 7., 6.],
[0, 0, 0, 0, 0, 0, 40., 26.],
[0, 0, 0, 0, 0, 0, 0, 7.],
[0, 0, 0, 0, 0, 0, 0, 0]])
site_hamiltonian = np.diag(site_energies) + couplings + couplings.T
evals, evecs = utils.sorted_eig(site_hamiltonian)
site_reorg_shift = 110.
site_reorg_energies = np.zeros(site_energies.size)
site_reorg_energies.fill(site_reorg_shift)
shifted_site_hamiltonian = site_hamiltonian + np.diag(site_reorg_energies)
shifted_evals, shifted_evecs = utils.sorted_eig(shifted_site_hamiltonian)
exciton_reorg_energies = os.exciton_reorg_energy(shifted_evecs, site_reorg_energies)
print evals
print shifted_evals - exciton_reorg_energies
print exciton_reorg_energies
for i,el in enumerate(evecs.flatten()):
print shifted_evecs.flatten()[i] + 0.0000001 > el > shifted_evecs.flatten()[i] - 0.0000001
for n in range(num_realisations):
print 'Calculating realisation ' + str(n + 1) + ' at time ' + str(
datetime.now().time())
# calculate Hamiltonian for this realisation ie. add site_shifts to average site energies and construct Hamiltonian
site_hamiltonian = np.diag(
average_site_energies + total_site_reorg_energy + site_shifts[n]
) + couplings + couplings.T # now including reorganisation shift
evals, evecs = utils.sorted_eig(
site_hamiltonian
) # make sure to return excitons in basis going from lowest to highest energy with sorted_eig
site_reorg_energies = np.zeros(site_hamiltonian.shape[0])
site_reorg_energies.fill(total_site_reorg_energy)
exciton_reorg_energies = np.zeros(site_hamiltonian.shape[0])
for i in range(site_hamiltonian.shape[0]):
exciton_reorg_energies[i] = os.exciton_reorg_energy(
evecs[i], site_reorg_energies) # calculate exciton reorg energies
evals = evals - exciton_reorg_energies # shift exciton energies down by exciton reorg energies
# calculate modified Redfield rates
rates = os.MRT_rate_PE545_quick(evals, evecs, g_site, g_site_dot,
g_site_dot_dot, total_site_reorg_energy,
temperature, integration_time)
# construct Liouvillian for system
liouvillian = np.zeros((rates.shape[0], rates.shape[1]))
for i, row in enumerate(rates.T):
liouvillian[i, i] = -np.sum(row)
liouvillian += rates
# calculate time evolution starting from provided initial state in exciton basis
init_dv = exciton_init_states[n]
dv_history = te.liouvillian_time_evolution(init_dv, liouvillian, duration,
lbf_dot = data['lbf_dot']
lbf_dot_dot = data['lbf_dot_dot']
time = data['time']
except IOError:
print 'Starting lbf calculations at ' + str(time_utils.getTime())
lbf_coeffs = os.lbf_coeffs(site_drude_reorg_energy, cutoff_freq, temperature, single_mode_params, 100)
lbf = os.site_lbf_ed(time, lbf_coeffs)
lbf_dot = os.site_lbf_dot_ed(time, lbf_coeffs)
lbf_dot_dot = os.site_lbf_dot_dot_ed(time, lbf_coeffs)
print 'Finished calculating lbfs at ' + str(time_utils.getTime())
np.savez(lbf_fn, lbf=lbf, lbf_dot=lbf_dot, lbf_dot_dot=lbf_dot_dot, time=time)
# calculate MRT rates
evals,evecs = utils.sorted_eig(hamiltonian[:6,:6])
exciton_reorg_energies = np.array([os.exciton_reorg_energy(exciton, site_reorg_energies) for exciton in evecs])
# print evals - exciton_reorg_energies
# evals,evecs = utils.sort_evals_evecs(evals-exciton_reorg_energies, evecs)
# print evals
# MRT_rates2 = os.modified_redfield_rates_general_unordered(evals-exciton_reorg_energies, evecs, lbf, lbf_dot, lbf_dot_dot, total_site_reorg_energy, temperature, time)
#
# liouvillian2 = MRT_rates2 - np.diag(np.sum(MRT_rates2, axis=0))
#
# print evals
# print MRT_rates2
print evals - exciton_reorg_energies
#MRT_rates,evals,evecs = os.modified_redfield_rates_general(evals-exciton_reorg_energies, evecs, lbf, lbf_dot, lbf_dot_dot, total_site_reorg_energy, temperature, time)
MRT_rates = os.modified_redfield_rates_general(evals-exciton_reorg_energies, evecs, lbf, lbf_dot, lbf_dot_dot, total_site_reorg_energy, temperature, time)[0]
print evals
total_site_reorg_energies = np.array(
[total_site_reorg_energy, total_site_reorg_energy])
rates_data = []
print 'Calculating rates with high energy modes....'
for V in coupling_values:
print 'Calculating rates for coupling ' + str(V)
rates = []
for i, delta_E in enumerate(delta_E_values):
site_hamiltonian = hamiltonian(delta_E, V) + np.diag(
total_site_reorg_energies
) # adjust site energies by reorganisation shift
evals, evecs = utils.sorted_eig(site_hamiltonian)
# calculate exciton reorganisation energies
exciton_reorg_energies = np.array([
os.exciton_reorg_energy(evecs[i], total_site_reorg_energies)
for i in range(site_hamiltonian.shape[0])
])
print exciton_reorg_energies
evals = evals - exciton_reorg_energies # adjust to bare exciton reorganisation energies
MRT = os.modified_redfield_rates(evals, evecs, g_site, g_site_dot,
g_site_dot_dot,
total_site_reorg_energy, temperature,
time)
rates.append(MRT[0, 1])
rates_data.append(rates)
#np.savez('../../data/modified_redfield_test_high_energy_modes_data.npz', delta_E_values=delta_E_values, coupling_values=coupling_values, rates=rates_data)
for i, rates in enumerate(rates_data):
plt.subplot(1, 3, i + 1)
plt.plot(delta_E_values, utils.WAVENUMS_TO_INVERSE_PS * np.array(rates))
liouvillians = np.zeros((num_realisations, average_site_CT_energies.size, average_site_CT_energies.size))
site_init_state = np.array([0.07, 0.14, 0.79, 0.4, 0.58, 0.56, 0, 0])
normalisation = np.sum(site_init_state)
for n in range(num_realisations):
if n % 100 == 0:
print "Calculating for realisation " + str(n)
hamiltonian = np.diag(energy_samples.T[n]) + couplings + couplings.T
site_hamiltonian = hamiltonian[:6,:6]
evals, evecs = utils.sorted_eig(site_hamiltonian)
exciton_reorg_energies = np.array([os.exciton_reorg_energy(exciton, site_reorg_energies) for exciton in evecs])
'''
# remove reorg energy and reorder evals/evecs from lowest to highest energy
evals, evecs = utils.sort_evals_evecs(evals-exciton_reorg_energies, evecs)
# calculate modified Redfield rates
MRT_rates = os.modified_redfield_rates_general(evals, evecs, lbf, lbf_dot, lbf_dot_dot, total_site_reorg_energy, temperature, time)[0]
# need to reorder exciton_reorg_energies too! easier to just recalculate with new evecs
exciton_reorg_energies = np.array([os.exciton_reorg_energy(exciton, site_reorg_energies) for exciton in evecs])
'''
'''
temporary to test that this reproduces the results for incorrect ordering of exciton levels