def liouvillian_build(H_0, A, gamma, wRC, T_C):
# Now this function has to construct the liouvillian so that it can be passed to mesolve
H_0, A, Chi, Xi = RCME_operators(H_0, A, gamma, beta_f(T_C))
L = 0
L -= spre(A * Chi)
L += sprepost(A, Chi)
L += sprepost(Chi, A)
L -= spost(Chi * A)
L += spre(A * Xi)
L += sprepost(A, Xi)
L -= sprepost(Xi, A)
L -= spost(Xi * A)
return L, Chi + Xi
def liouvillian_build_new(H_0, A, gamma, wRC, T_C):
# Now this function has to construct the liouvillian so that it can be passed to mesolve
H_0, A, Chi, Xi = RCME_operators(H_0, A, gamma, beta_f(T_C))
Z = Chi + Xi
Z_dag = Z.dag()
L = 0
#L+=spre(A*Z_dag)
#L-=sprepost(A, Z)
#L-=sprepost(Z_dag, A)
#L+=spost(Z_dag*A)
L -= spre(A * Z_dag)
L += sprepost(A, Z)
L += sprepost(Z_dag, A)
L -= spost(Z * A)
print("new L built")
return L, Z
def L_wc_analytic(detuning=0.,
Rabi=0,
alpha=0.,
w0=0.,
Gamma=0.,
T=0.,
tol=1e-7):
energies, states = exciton_states(detuning, Rabi)
dark_proj = states[0] * states[0].dag()
bright_proj = states[1] * states[1].dag()
ct_p = states[1] * states[0].dag()
ct_m = states[0] * states[1].dag()
cross_term = (ct_p + ct_m)
epsilon = -detuning
V = Rabi / 2
eta = sqrt(epsilon**2 + 4 * V**2)
# Bath 1 (only one bath)
G = (lambda x: (DecayRate(x,
beta_f(T),
_J_underdamped,
Gamma,
w0,
imag_part=True,
alpha=alpha,
tol=tol)))
G_0 = G(0.)
G_p = G(eta)
G_m = G(-eta)
site_1 = (0.5 / eta) * ((eta + epsilon) * bright_proj +
(eta - epsilon) * dark_proj + 2 * V * cross_term)
Z_1 = (0.5 / eta) * (G_0 * ((eta + epsilon) * bright_proj +
(eta - epsilon) * dark_proj) + 2 * V *
(ct_p * G_p + ct_m * G_m))
L = -qt.spre(site_1 * Z_1) + qt.sprepost(Z_1, site_1)
L += -qt.spost(Z_1.dag() * site_1) + qt.sprepost(site_1, Z_1.dag())
return L
def L_non_rwa(H_vib,
A,
w_0,
Gamma,
T_EM,
J,
principal=False,
silent=False,
alpha=0.,
tol=1e-5):
ti = time.time()
beta = beta_f(T_EM)
eVals, eVecs = H_vib.eigenstates()
#J=J_minimal # J_minimal(omega, Gamma, omega_0)
d_dim = len(eVals)
G = 0
for i in range(d_dim):
for j in range(d_dim):
eta = eVals[i] - eVals[j]
s = eVecs[i] * (eVecs[j].dag())
#print A.matrix_element(eVecs[i].dag(), eVecs[j])
overlap = A.matrix_element(eVecs[i].dag(), eVecs[j])
s *= A.matrix_element(eVecs[i].dag(), eVecs[j])
s *= DecayRate(eta,
beta,
J,
Gamma,
w_0,
imag_part=principal,
alpha=alpha,
tol=tol)
G += s
G_dag = G.dag()
# Initialise liouvilliian
L = qt.spre(A * G) - qt.sprepost(G, A)
L += qt.spost(G_dag * A) - qt.sprepost(A, G_dag)
if not silent:
print(("Calculating non-RWA Liouvilliian took {} seconds.".format(
time.time() - ti)))
return -L