def test_compare_solvers_steadystate():
"""
correlation: comparing me and es for oscillator in steady-state
"""
N = 20
a = destroy(N)
H = a.dag() * a
G1 = 0.75
n_th = 2.00
c_ops = [np.sqrt(G1 * (1 + n_th)) * a, np.sqrt(G1 * n_th) * a.dag()]
taulist = np.linspace(0, 5.0, 100)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
corr1 = correlation_2op_1t(H,
None,
taulist,
c_ops,
a.dag(),
a,
solver="me")
corr2 = correlation_2op_1t(H,
None,
taulist,
c_ops,
a.dag(),
a,
solver="es")
assert_(max(abs(corr1 - corr2)) < 1e-4)
def test_correlation_2op_1t_known_cases(solver,
state,
is_e_op_hermitian,
w,
gamma,
):
"""This test compares the output correlation_2op_1 solution to an analytical
solution."""
a = qutip.destroy(_equivalence_dimension)
x = (a + a.dag())/np.sqrt(2)
H = w * a.dag() * a
a_op = x if is_e_op_hermitian else a
b_op = x if is_e_op_hermitian else a.dag()
c_ops = [np.sqrt(gamma) * a]
times = np.linspace(0, 1, 30)
# Handle the case state==None when computing expt values
rho0 = state if state else qutip.steadystate(H, c_ops)
if is_e_op_hermitian:
# Analitycal solution for x,x as operators.
base = 0
base += qutip.expect(a*x, rho0)*np.exp(-1j*w*times - gamma*times/2)
base += qutip.expect(a.dag()*x, rho0)*np.exp(1j*w*times - gamma*times/2)
base /= np.sqrt(2)
else:
# Analitycal solution for a,adag as operators.
base = qutip.expect(a*a.dag(), rho0)*np.exp(-1j*w*times - gamma*times/2)
cmp = qutip.correlation_2op_1t(H, state, times, c_ops, a_op, b_op, solver=solver)
np.testing.assert_allclose(base, cmp, atol=0.25 if solver == 'mc' else 2e-5)
def test_compare_solvers_steadystate():
"""
correlation: comparing me and es for oscillator in steady-state
"""
N = 20
a = destroy(N)
H = a.dag() * a
G1 = 0.75
n_th = 2.00
c_ops = [np.sqrt(G1 * (1 + n_th)) * a, np.sqrt(G1 * n_th) * a.dag()]
taulist = np.linspace(0, 5.0, 100)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
corr1 = correlation_2op_1t(H, None, taulist, c_ops, a.dag(), a,
solver="me")
corr2 = correlation_2op_1t(H, None, taulist, c_ops, a.dag(), a,
solver="es")
assert_(max(abs(corr1 - corr2)) < 1e-4)
import numpy as np import matplotlib.pyplot as plt import qutip times = np.linspace(0, 10, 200) a = qutip.destroy(10) x = a.dag() + a H = a.dag() * a corr1 = qutip.correlation_2op_1t(H, None, times, [np.sqrt(0.5) * a], x, x) corr2 = qutip.correlation_2op_1t(H, None, times, [np.sqrt(1.0) * a], x, x) corr3 = qutip.correlation_2op_1t(H, None, times, [np.sqrt(2.0) * a], x, x) plt.plot(times, np.real(corr1), times, np.real(corr2), times, np.real(corr3)) plt.xlabel(r'Time $t$') plt.ylabel(r'Correlation $\left<x(t)x(0)\right>$') plt.show()