def liouvillian_time_evolution(init_density_vector, liouvillian, duration, timestep, trace_basis=None, wave_nums=True):
if wave_nums:
liouvillian = utils.hamiltonian_to_picosecs(liouvillian)
timestep_operator = la.expm(liouvillian*timestep)
density_vector = init_density_vector
dv_history = []
dv_history.append(density_vector)
for step in range(int(duration/timestep)):
density_vector = np.dot(timestep_operator, density_vector)
dv_history.append(density_vector)
return np.array(dv_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)