def test_discrete_level_model_fermionic_bath(self, evo, liouvillianize):
dlm = DiscreteLevelCurrentModel(
gamma=0.01,
W=1,
T=0.025851991,
lmax=10,
)
H_sys = hamiltonian_to_sys(dlm.H, evo, liouvillianize)
ck_plus, vk_plus, ck_minus, vk_minus = dlm.bath_coefficients()
options = Options(
nsteps=15_000,
store_states=True,
rtol=1e-7,
atol=1e-7,
)
bath = FermionicBath(dlm.Q, ck_plus, vk_plus, ck_minus, vk_minus)
# for a single impurity we converge with max_depth = 2
hsolver = HEOMSolver(H_sys, bath, 2, options=options)
tlist = [0, 600]
result = hsolver.run(dlm.rho(), tlist, ado_return=True)
current = dlm.state_current(result.ado_states[-1])
analytic_current = dlm.analytic_current()
np.testing.assert_allclose(analytic_current, current, rtol=1e-3)
rho_final, ado_state = hsolver.steady_state()
current = dlm.state_current(ado_state)
analytic_current = dlm.analytic_current()
np.testing.assert_allclose(analytic_current, current, rtol=1e-3)
def test_underdamped_pure_dephasing_model_underdamped_bath(
self, atol=1e-3):
udm = UnderdampedPureDephasingModel(
lam=0.1,
gamma=0.05,
w0=1,
T=1 / 0.95,
Nk=2,
)
bath = UnderDampedBath(
Q=udm.Q,
lam=udm.lam,
T=udm.T,
Nk=udm.Nk,
gamma=udm.gamma,
w0=udm.w0,
)
options = Options(nsteps=15000, store_states=True)
hsolver = HEOMSolver(udm.H, bath, 14, options=options)
tlist = np.linspace(0, 10, 21)
result = hsolver.run(udm.rho(), tlist)
test = udm.state_results(result.states)
expected = udm.analytic_results(tlist)
np.testing.assert_allclose(test, expected, atol=atol)
rho_final, ado_state = hsolver.steady_state()
test = udm.state_results([rho_final])
expected = udm.analytic_results([5000])
np.testing.assert_allclose(test, expected, atol=atol)
assert rho_final == ado_state.extract(0)
def test_pure_dephasing_model_bosonic_bath(self,
evo,
combine,
liouvillianize,
atol=1e-3):
dlm = DrudeLorentzPureDephasingModel(
lam=0.025,
gamma=0.05,
T=1 / 0.95,
Nk=2,
)
ck_real, vk_real, ck_imag, vk_imag = dlm.bath_coefficients()
H_sys = hamiltonian_to_sys(dlm.H, evo, liouvillianize)
bath = BosonicBath(dlm.Q, ck_real, vk_real, ck_imag, vk_imag)
options = Options(nsteps=15000, store_states=True)
hsolver = HEOMSolver(H_sys, bath, 14, options=options)
tlist = np.linspace(0, 10, 21)
result = hsolver.run(dlm.rho(), tlist)
test = dlm.state_results(result.states)
expected = dlm.analytic_results(tlist)
np.testing.assert_allclose(test, expected, atol=atol)
rho_final, ado_state = hsolver.steady_state()
test = dlm.state_results([rho_final])
expected = dlm.analytic_results([100])
np.testing.assert_allclose(test, expected, atol=atol)
assert rho_final == ado_state.extract(0)
def test_integration_error(self):
dlm = DrudeLorentzPureDephasingModel(
lam=0.025,
gamma=0.05,
T=1 / 0.95,
Nk=2,
)
ck_real, vk_real, ck_imag, vk_imag = dlm.bath_coefficients()
bath = BosonicBath(dlm.Q, ck_real, vk_real, ck_imag, vk_imag)
options = Options(nsteps=10)
hsolver = HEOMSolver(dlm.H, bath, 14, options=options)
with pytest.raises(RuntimeError) as err:
hsolver.run(dlm.rho(), tlist=[0, 10])
assert str(err.value) == (
"HEOMSolver ODE integration error. Try increasing the nsteps given"
" in the HEOMSolver options (which increases the allowed substeps"
" in each step between times given in tlist).")
def test_discrete_level_model_lorentzian_baths(self,
bath_cls,
analytic_current,
atol=1e-3):
dlm = DiscreteLevelCurrentModel(
gamma=0.01,
W=1,
T=0.025851991,
lmax=10,
)
options = Options(
nsteps=15_000,
store_states=True,
rtol=1e-7,
atol=1e-7,
)
bath_l = bath_cls(
dlm.Q,
gamma=dlm.gamma,
w=dlm.W,
T=dlm.T,
mu=dlm.theta / 2,
Nk=dlm.lmax,
)
bath_r = bath_cls(
dlm.Q,
gamma=dlm.gamma,
w=dlm.W,
T=dlm.T,
mu=-dlm.theta / 2,
Nk=dlm.lmax,
)
# for a single impurity we converge with max_depth = 2
hsolver = HEOMSolver(dlm.H, [bath_r, bath_l], 2, options=options)
tlist = [0, 600]
result = hsolver.run(dlm.rho(), tlist, ado_return=True)
current = dlm.state_current(result.ado_states[-1])
# analytic_current = dlm.analytic_current()
np.testing.assert_allclose(analytic_current, current, rtol=1e-3)
rho_final, ado_state = hsolver.steady_state()
current = dlm.state_current(ado_state)
# analytic_current = dlm.analytic_current()
np.testing.assert_allclose(analytic_current, current, rtol=1e-3)
def test_pure_dephasing_model_drude_lorentz_baths(self,
terminator,
bath_cls,
atol=1e-3):
dlm = DrudeLorentzPureDephasingModel(
lam=0.025,
gamma=0.05,
T=1 / 0.95,
Nk=2,
)
bath = bath_cls(
Q=dlm.Q,
lam=dlm.lam,
gamma=dlm.gamma,
T=dlm.T,
Nk=dlm.Nk,
)
if terminator:
_, terminator_op = bath.terminator()
H_sys = liouvillian(dlm.H) + terminator_op
else:
H_sys = dlm.H
options = Options(nsteps=15000, store_states=True)
hsolver = HEOMSolver(H_sys, bath, 14, options=options)
tlist = np.linspace(0, 10, 21)
result = hsolver.run(dlm.rho(), tlist)
test = dlm.state_results(result.states)
expected = dlm.analytic_results(tlist)
np.testing.assert_allclose(test, expected, atol=atol)
rho_final, ado_state = hsolver.steady_state()
test = dlm.state_results([rho_final])
expected = dlm.analytic_results([100])
np.testing.assert_allclose(test, expected, atol=atol)
assert rho_final == ado_state.extract(0)
def test_ado_return_and_ado_init(self, ado_format):
dlm = DrudeLorentzPureDephasingModel(
lam=0.025,
gamma=0.05,
T=1 / 0.95,
Nk=2,
)
ck_real, vk_real, ck_imag, vk_imag = dlm.bath_coefficients()
bath = BosonicBath(dlm.Q, ck_real, vk_real, ck_imag, vk_imag)
options = Options(nsteps=15_000, store_states=True)
hsolver = HEOMSolver(dlm.H, bath, 6, options=options)
tlist_1 = [0, 1, 2]
result_1 = hsolver.run(dlm.rho(), tlist_1, ado_return=True)
tlist_2 = [2, 3, 4]
rho0 = result_1.ado_states[-1]
if ado_format == "numpy":
rho0 = rho0._ado_state # extract the raw numpy array
result_2 = hsolver.run(
rho0,
tlist_2,
ado_return=True,
ado_init=True,
)
tlist_full = tlist_1 + tlist_2[1:]
result_full = hsolver.run(dlm.rho(), tlist_full, ado_return=True)
times_12 = result_1.times + result_2.times[1:]
times_full = result_full.times
assert times_12 == tlist_full
assert times_full == tlist_full
ado_states_12 = result_1.ado_states + result_2.ado_states[1:]
ado_states_full = result_full.ado_states
assert len(ado_states_12) == len(tlist_full)
assert len(ado_states_full) == len(tlist_full)
for ado_12, ado_full in zip(ado_states_12, ado_states_full):
for label in hsolver.ados.labels:
np.testing.assert_allclose(
ado_12.extract(label).full(),
ado_full.extract(label).full(),
atol=1e-6,
)
states_12 = result_1.states + result_2.states[1:]
states_full = result_full.states
assert len(states_12) == len(tlist_full)
assert len(states_full) == len(tlist_full)
for ado_12, state_12 in zip(ado_states_12, states_12):
assert ado_12.rho == state_12
for ado_full, state_full in zip(ado_states_full, states_full):
assert ado_full.rho == state_full
expected = dlm.analytic_results(tlist_full)
test_12 = dlm.state_results(states_12)
np.testing.assert_allclose(test_12, expected, atol=1e-3)
test_full = dlm.state_results(states_full)
np.testing.assert_allclose(test_full, expected, atol=1e-3)