def test_compare_solvers_coherent_state_legacy():
"""
correlation: legacy me and es for oscillator in coherent initial 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()]
rho0 = coherent_dm(N, np.sqrt(4.0))
taulist = np.linspace(0, 5.0, 100)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
corr1 = correlation(H,
rho0,
None,
taulist,
c_ops,
a.dag(),
a,
solver="me")
corr2 = correlation(H,
rho0,
None,
taulist,
c_ops,
a.dag(),
a,
solver="es")
assert_(max(abs(corr1 - corr2)) < 1e-4)
def get_qutip_peierls_kubo(J, nsites, ph_levels, omega, g, temperature,
time_series):
clist = get_clist(nsites, ph_levels)
blist = get_blist(nsites, ph_levels)
qn_idx = get_qnidx(ph_levels, nsites)
H = get_peierls_hamiltonian(nsites, J, omega, g, clist,
blist).extract_states(qn_idx)
init_state = (-temperature.to_beta() * H).expm().unit()
holstein_terms = []
peierls_terms = []
for i in range(nsites):
next_i = (i + 1) % nsites
holstein_terms.append(J * clist[i].dag() * clist[next_i])
holstein_terms.append(-J * clist[i] * clist[next_i].dag())
peierls_terms.append(g * omega * clist[i].dag() * clist[next_i] *
(blist[i].dag() + blist[i]))
peierls_terms.append(-g * omega * clist[i] * clist[next_i].dag() *
(blist[i].dag() + blist[i]))
j_oper1 = sum(holstein_terms).extract_states(qn_idx)
j_oper2 = sum(peierls_terms).extract_states(qn_idx)
# Add negative signs because j is taken to be real
corr1 = -qutip.correlation(H, init_state, [0], time_series, [], j_oper1,
j_oper1)[0]
corr2 = -qutip.correlation(H, init_state, [0], time_series, [], j_oper1,
j_oper2)[0]
corr3 = -qutip.correlation(H, init_state, [0], time_series, [], j_oper2,
j_oper1)[0]
corr4 = -qutip.correlation(H, init_state, [0], time_series, [], j_oper2,
j_oper2)[0]
corr = corr1 + corr2 + corr3 + corr4
return corr, np.array([corr1, corr2, corr3, corr4]).T
def get_exact_autocorr(mol_list, temperature, time_series):
nsites = len(mol_list)
J = mol_list.j_constant.as_au()
ph = mol_list[0].dmrg_phs[0]
ph_levels = ph.n_phys_dim
omega = ph.omega[0]
g = -ph.coupling_constant
clist = get_clist(nsites, ph_levels)
blist = get_blist(nsites, ph_levels)
qn_idx = get_qnidx(ph_levels, nsites)
H = get_hamiltonian(nsites, J, omega, g, clist,
blist).extract_states(qn_idx)
init_state = (-temperature.to_beta() * H).expm().unit()
terms = []
for i in range(nsites - 1):
terms.append(clist[i].dag() * clist[i + 1])
terms.append(-clist[i] * clist[i + 1].dag())
j_oper = sum(terms).extract_states(qn_idx)
corr = qutip.correlation(H, init_state, [0], time_series, [], j_oper,
j_oper)[0]
return corr
def get_qutip_holstein_kubo(model, temperature, time_series):
nsites = len(model)
J = model.j_constant
ph = model[0].ph_list[0]
ph_levels = ph.n_phys_dim
omega = ph.omega[0]
g = -ph.coupling_constant
clist = get_clist(nsites, ph_levels)
blist = get_blist(nsites, ph_levels)
qn_idx = get_qnidx(ph_levels, nsites)
H = get_holstein_hamiltonian(nsites, J, omega, g, clist,
blist).extract_states(qn_idx)
init_state = (-temperature.to_beta() * H).expm().unit()
terms = []
for i in range(nsites - 1):
terms.append(J * clist[i].dag() * clist[i + 1])
terms.append(-J * clist[i] * clist[i + 1].dag())
j_oper = sum(terms).extract_states(qn_idx)
# Add the negative sign because j is taken to be real
return -qutip.correlation(H, init_state, [0], time_series, [], j_oper,
j_oper)[0]
def test_compare_solvers_steadystate_legacy():
"""
correlation: legacy 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(H, None, None, taulist, c_ops, a.dag(), a,
solver="me")
corr2 = correlation(H, None, None, taulist, c_ops, a.dag(), a,
solver="es")
assert_(max(abs(corr1 - corr2)) < 1e-4)
