def set_quantum_sys(self):
"""
Initialize quantum propagator
:param self:
:return:
"""
omega = 1.
self.quant_sys = SplitOpWignerMoyal(
t=0,
dt=0.05,
x_grid_dim=256,
x_amplitude=10.,
p_grid_dim=256,
p_amplitude=10.,
# kinetic energy part of the hamiltonian
k=lambda p: 0.5 * p**2,
# potential energy part of the hamiltonian
v=lambda x: 0.5 * (omega * x)**2,
# these functions are used for evaluating the Ehrenfest theorems
x_rhs=lambda p: p,
p_rhs=lambda x, p: -omega**2 * x,
)
# set randomised initial condition
sigma = np.random.uniform(1., 3.)
p0 = np.random.uniform(-3., 3.)
x0 = np.random.uniform(-3., 3.)
self.quant_sys.set_wignerfunction(lambda x, p: np.exp(-sigma * (
x - x0)**2 - (1. / sigma) * (p - p0)**2))
# kinetic energy part of the hamiltonian
K="0.5 * {P} ** 2",
# potential energy part of the hamiltonian
V="0.5 * {X} ** 4",
)
print("Calculating the Gibbs state...")
gibbs_state = SplitOpWignerBloch(**qsys_params).get_thermal_state()
# Propagate this state via the Wigner-Moyal equation
print(
"Check that the obtained Gibbs state is stationary under the Wigner-Moyal propagation..."
)
propagator = SplitOpWignerMoyal(**qsys_params)
final_state = propagator.set_wignerfunction(gibbs_state).propagate(3000)
##############################################################################
#
# Plot the results
#
##############################################################################
from wigner_normalize import WignerSymLogNorm
# save common plotting parameters
plot_params = dict(
origin='lower',
extent=[
propagator.X.min(),