def markovian_master_eqn_RK4(init_density_matrix, hamiltonian, duration, timestep, trace_basis=None, jump_operators=None, hamiltonianInWaveNums=True):
if hamiltonianInWaveNums:
hamiltonian = utils.WAVENUMS_TO_INVERSE_PS * hamiltonian
density_matrix = init_density_matrix
dm_history = []
if trace_basis:
dm_history.append(utils.partial_trace(density_matrix, trace_basis))
else:
dm_history.append(density_matrix)
for step in range(0, int(duration/timestep)):
# if step % 100 == 0:
# print "Reached step " + str(step)
k1 = timestep * master_equation(density_matrix, hamiltonian, jump_operators)
k2 = timestep * master_equation(density_matrix + (0.5*k1), hamiltonian, jump_operators)
k3 = timestep * master_equation(density_matrix + (0.5*k2), hamiltonian, jump_operators)
k4 = timestep * master_equation(density_matrix + k3, hamiltonian, jump_operators)
density_matrix = density_matrix + (1./6.) * (k1 + 2.*k2 + 2.*k3 + k4)
if trace_basis:
dm_history.append(utils.partial_trace(density_matrix, trace_basis))
else:
dm_history.append(density_matrix)
return dm_history
def von_neumann_eqn(init_density_matrix, hamiltonian, duration, timestep, trace_basis=None, wave_nums=True):
if wave_nums:
hamiltonian = utils.hamiltonian_to_picosecs(hamiltonian)
timestep_operator = la.expm(-1j*hamiltonian*timestep)
timestep_operator_dagger = timestep_operator.conj().T
density_matrix = init_density_matrix
dm_history = []
if trace_basis:
dm_history.append(utils.partial_trace(density_matrix, trace_basis))
else:
dm_history.append(density_matrix)
for step in range(int(duration/timestep)):
density_matrix = np.dot(np.dot(timestep_operator, density_matrix), timestep_operator_dagger)
if trace_basis:
dm_history.append(utils.partial_trace(density_matrix, trace_basis))
else:
dm_history.append(density_matrix)
return np.array(dm_history)
print 'Calculations for v = ' + str(v)
#model.mode_coupling = v
#model.N = v
model.vib_damping_rate = v
temp_current = np.zeros(num_data_pts)
#temp_current_cs = np.zeros(num_data_pts)
for j,e in enumerate(energy_gap_range):
model.energy_gap = e
L = model.liouvillian()
dm_pops = np.eye(3*model.vib_basis_size).flatten()
ss_vec = utils.stationary_state(L, dm_pops)
ss_mat = ss_vec.copy()
ss_mat.shape = np.sqrt(ss_mat.shape[0]), np.sqrt(ss_mat.shape[0])
ss_el = utils.partial_trace(ss_mat, utils.orthog_basis_set(model.vib_basis_size))
temp_current[j] = model.Gamma_R * ss_el[2,2]
#temp_current_cs[j] = cs.mean(L, model.jump_liouvillian(), ss_vec, dm_pops)
current[i] = temp_current
plt.plot(energy_gap_range, current[i], label=v)
#np.savez('../../data/dimer_vib_energy_gap_current_mode_coupling_data.npz', energy_gap_range=energy_gap_range, current=current, mode_couplings=mode_couplings)
#np.savez('../../data/dimer_vib_energy_gap_current_thermal_occupation_data.npz', energy_gap_range=energy_gap_range, current=current, thermal_occupations=thermal_occupations)
np.savez('../../data/dimer_vib_energy_gap_current_mode_damping_data.npz', energy_gap_range=energy_gap_range, current=current, mode_dampings=mode_dampings)
#plt.plot(energy_gap_range, current_cs)
plt.legend()
plt.show()
