def test_brownian():
lambda_0 = 0.05 # reorganization energy (dimensionless)
omega_0 = 1.0 # vibrational frequency (dimensionless)
zeta = 0.5 # damping constant (dimensionless)
max_tier = 5
omega_1 = np.sqrt(omega_0**2 - zeta**2*0.25)
J = pyheom.Brownian(lambda_0, zeta, omega_0)
corr_dict = pyheom.noise_decomposition(
J,
T = 1, # temperature (dimensionless)
type_LTC = 'PSD',
n_PSD = 1,
type_PSD = 'N-1/N'
)
s = corr_dict['s'].toarray()
a = corr_dict['a'].toarray()
gamma = corr_dict['gamma'].toarray()
delta = 0
h = np.array([[omega_1, 0],
[0, 0]])
op = np.array([[0, 1],
[1, 0]])
max_terms = 3
corr = Correlation(k_max=max_terms, beta=1)
corr.symm_coeff = np.diag(s)
corr.asymm_coeff = np.diag(a)
corr.exp_coeff = np.diag(gamma)
corr.delta_coeff = delta
corr.print()
heom = Hierachy([max_tier] * max_terms, h, op, corr)
rho_0 = np.zeros((2, 2))
rho_0[0, 0] = 1
init_wfn = heom.gen_extended_rho(rho_0)
solver = MultiLayer(init_wfn, heom.diff())
# Define the obersevable of interest
dat = []
for n, (time, r) in enumerate(solver.propagator(
steps=5000,
ode_inter=0.01,
)):
if n % 100 == 0:
rho = np.reshape(r, (-1, 4))
for n, _rn in enumerate(rho):
if n == 0:
flat_data = [time] + list(rho[0])
dat.append(flat_data)
if n <= 0:
print("Time: {} ; {}: {}".format(time, n, _rn[0] + _rn[-1]))
return np.array(dat)
def test_drude():
from minitn.heom.noise import Drude
from minitn.lib.units import Quantity
# System
e = Quantity(100, 'cm-1').value_in_au
v = Quantity(50, 'cm-1').value_in_au
# Bath
corr2 = Correlation(k_max=1)
corr2.symm_coeff = [0.0] # [4.66691921e+01 * 9.24899189e+01]
corr2.asymm_coeff = [0.0] # [4.66691921e+01 * -2.35486582e+01]
corr2.exp_coeff = [1.0]
corr2.delta_coeff = 0.0 # delta_coeff()
corr2.print()
h = np.array([[e, v],
[v, 0]])
op = np.array([[1, 0],
[0, -1]])
# Superparameters
max_tier = 5 # (number of possble values for each n_k in the extended rho)
heom = Hierachy([max_tier], h, op, corr2)
phi = np.array([1, 0])
rho_0 = np.tensordot(phi, phi, axes=0)
init_rho = heom.gen_extended_rho(rho_0)
solver = MultiLayer(init_rho, heom.diff())
# Define the obersevable of interest
dat = []
for n, (time, r) in enumerate(solver.propagator(
steps=20000,
ode_inter=0.1,
)):
if n % 100 == 0:
rho = np.reshape(r, (-1, 4))
for n, _ in enumerate(rho):
if n == 0:
flat_data = [time] + list(rho[0])
dat.append(flat_data)
print('Time: {}; rho: {} {} {} {}'.format(*flat_data))
np.savetxt('test.dat', np.array(dat, dtype=np.complex128))
return np.array(dat)
def test_drude():
# Type settings
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.diag(corr_dict['s'].toarray())
corr.asymm_coeff = np.diag(corr_dict['a'].toarray())
corr.exp_coeff = np.diag(corr_dict['gamma'].toarray())
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
n_dims = [max_tier] * max_terms
hseom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
root = simple_hseom(init_wfns, n_dims)
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in hseom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = MultiLayer(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.atol = 1.e-7
solver.rtol = 1.e-7
# Define the obersevable of interest
dat = []
for n, (time,
r) in enumerate(solver.propagator(
steps=count,
ode_inter=dt_unit,
)):
try:
if n % callback_interval == 0:
wfns = np.reshape(r.array, (-1, n_state**2))[0]
print("Time: {}; |c|: {}".format(time,
np.linalg.norm(wfns)))
f = np.reshape(wfns, (n_state, n_state))
rho = sum(np.outer(i, i) for i in f)
flat_data = [time] + list(np.reshape(rho, -1))
dat.append(flat_data)
except:
break
return np.array(dat)
def test_simple():
# Type settings
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.diag(corr_dict['s'].toarray())
corr.asymm_coeff = np.diag(corr_dict['a'].toarray())
corr.exp_coeff = np.diag(corr_dict['gamma'].toarray())
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
root = simple_heom(rho_0, n_dims)
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
#solver = ProjectorSplitting(root, all_terms)
solver = MultiLayer(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.atol = 1.e-7
solver.rtol = 1.e-7
# Define the obersevable of interest
dat = []
for n, (time,
r) in enumerate(solver.propagator(
steps=count,
ode_inter=dt_unit,
)):
try:
if n % callback_interval == 0:
rho = np.reshape(r.array, (-1, 4))
flat_data = [time] + list(rho[0])
dat.append(flat_data)
print("Time: {}; Tr rho_0: {}".format(
time, rho[0, 0] + rho[0, -1]))
except:
break
return np.array(dat)
def test_train(fname=None):
# Type settings
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.diag(corr_dict['s'].toarray())
corr.asymm_coeff = np.diag(corr_dict['a'].toarray())
corr.exp_coeff = np.diag(corr_dict['gamma'].toarray())
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt TT
tensor_train = tensor_train_template(rho_0, n_dims)
root = tensor_train[0]
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = MultiLayer(root, all_terms)
#solver = ProjectorSplitting(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.atol = 1.e-7
solver.rtol = 1.e-7
solver.ps_method = 'split-unite'
projector = np.zeros((max_tier, 1))
projector[0] = 1.0
logger = Logger(filename=fname, level='info').logger
for n, (time, _) in enumerate(
solver.propagator(steps=count, ode_inter=dt_unit, split=False)):
if n % callback_interval == 0:
head = root.array
for t in tensor_train[1:]:
spf = Tensor.partial_product(t.array, 1, projector, 0)
head = Tensor.partial_product(head, head.ndim - 1, spf, 0)
rho = np.reshape(head, (4, -1))[:, 0]
logger.info("{} {} {} {} {}".format(time, rho[0], rho[1], rho[2],
rho[3]))
return
def test_drude(fname=None):
# Type settings
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.diag(corr_dict['s'].toarray())
corr.asymm_coeff = np.diag(corr_dict['a'].toarray())
corr.exp_coeff = np.diag(corr_dict['gamma'].toarray())
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
root = simple_heom(rho_0, n_dims)
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = ProjectorSplitting(root, all_terms)
solver.ode_method = 'DOP853'
solver.snd_order = False
solver.atol = 1.e-7
solver.rtol = 1.e-7
# Define the obersevable of interest
logger = Logger(filename=fname, level='info').logger
for n, (time, r) in enumerate(solver.propagator(
steps=count,
ode_inter=dt_unit,
)):
if n % callback_interval == 0:
rho = np.reshape(r.array, (-1, 4))
logger.info("{} {} {} {} {}".format(time, rho[0, 0], rho[0, 1], rho[0, 2], rho[0, 3]))
print("Time: {}; Tr rho_0: {}".format(time, rho[0, 0] + rho[0, -1]))
return
def test_drude_train():
eta = 0.05 # reorganization energy (dimensionless)
gamma_c = 0.05 # vibrational frequency (dimensionless)
max_tier = 10
max_terms = 3
J = pyheom.Drudian(eta, gamma_c)
corr_dict = pyheom.noise_decomposition(
J,
T=1, # temperature (dimensionless)
type_LTC='PSD',
n_PSD=max_terms - 1,
type_PSD='N-1/N')
s = corr_dict['s'].toarray()
a = corr_dict['a'].toarray()
gamma = corr_dict['gamma'].toarray()
delta = 0
omega_1 = 0.05
omega_2 = 0.02
H = np.array([[omega_1, omega_2], [omega_2, 0]])
V = np.array([[0, 0], [0, 1]])
corr = Correlation(k_max=max_terms, beta=1)
corr.symm_coeff = np.diag(s)
corr.asymm_coeff = np.diag(a)
corr.exp_coeff = np.diag(gamma)
corr.delta_coeff = delta
corr.print()
heom = Hierachy([max_tier] * max_terms, H, V, corr)
rho_0 = np.zeros((2, 2))
rho_0[0, 0] = 1
# TT HEOM
tensor_train = tensor_train_template(rho_0, [max_tier] * max_terms,
rank=max_tier)
root = tensor_train[0]
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = MultiLayer(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.max_ode_steps = 100000
# Define the obersevable of interest
projector = np.zeros((max_tier, 1))
projector[0] = 1.0
dat = []
for n, (time,
r) in enumerate(solver.propagator(
steps=20000,
ode_inter=0.01,
)):
head = root.array
for t in tensor_train[1:]:
spf = Tensor.partial_product(t.array, 1, projector, 0)
head = Tensor.partial_product(head, head.ndim - 1, spf, 0)
rho = np.reshape(head, (4, -1))[:, 0]
flat_data = [time] + list(rho)
dat.append(flat_data)
print("Time {} | Pop_1 {} | Total {}".format(time, rho[0],
rho[0] + rho[-1]))
return np.array(dat)
# System
n_state = 2
H = np.array([[1.0, 1.0], [1.0, -1.0]])
#H = np.array([[0.0, 0.5], [0.5, 0.0]])
V = np.array([[1.0, 0.0], [0.0, -1.0]])
# Init state
p0 = 1.0
rho_0 = np.array([[p0, 0.0], [0.0, 1.0 - p0]])
# Bath
eta = 2.5 # reorganization energy (dimensionless)
gamma_c = 2.5 # vibrational frequency (dimensionless)
max_tier = 10
max_terms = 3
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.array([2.0767159490388725, 4.858236601790542, 7.778227240752226])
corr.asymm_coeff = np.array([-0.0625, 0.0, 0.0])
corr.exp_coeff = np.array([2.5, 6.305939144224808, 19.499618752922675])
corr.delta_coeff = 0.0 # delta_coeff
dt_unit = 0.01
callback_interval = 100
count = 500000
def test_train(fname=None):
# HEOM metas
corr.print()
n_dims = [max_tier] * max_terms
rho_0 = np.array([[0.5, 0.5], [0.5, 0.5]])
dt_unit = 0.001
callback_interval = 100
count = 50000
# Bath
# C = g**2 (coth (beta omega / 2)) cos wt - ig**2 sin wt
max_terms = 2
max_tier = 20
omega = 0.05
g = 0.1
beta = 0.1
corr = Correlation(k_max=max_terms)
temp_factor = 1.0 / np.tanh(beta * omega / 2)
corr.symm_coeff = np.array(
[g**2 * (temp_factor + 1) / 2.0, g**2 * (temp_factor - 1) / 2.0])
corr.asymm_coeff = np.array([0.0, 0.0])
corr.exp_coeff = np.array([1.0j * omega, -1.0j * omega])
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
def test_delta(fname=None):
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
# System
n_state = 2
H = np.array([[1.0, 1.0], [1.0, -1.0]])
#H = np.array([[0.0, 0.5], [0.5, 0.0]])
V = np.array([[1.0, 0.0], [0.0, -1.0]])
# Init state
p0 = 1.0
rho_0 = np.array([[p0, 0.0], [0.0, 1.0 - p0]])
# Bath
eta = 0.25 # reorganization energy (dimensionless)
gamma_c = 0.25 # vibrational frequency (dimensionless)
max_tier = 10
max_terms = 3
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.array(
[0.4973931166166882, 0.041010943929914466, 0.0765163269642356])
corr.asymm_coeff = np.array([-0.0625, 0.0, 0.0])
corr.exp_coeff = np.array([0.25, 6.305939144224808, 19.499618752922675])
corr.delta_coeff = 0.0 # delta_coeff
dt_unit = 0.01
callback_interval = 100
count = 500000
def test_train(fname=None):
# HEOM metas
corr.print()
def test_drude_tree():
eta = 0.05 # reorganization energy (dimensionless)
gamma_c = 0.05 # vibrational frequency (dimensionless)
max_tier = 10
max_terms = 3
J = pyheom.Drudian(eta, gamma_c)
corr_dict = pyheom.noise_decomposition(
J,
T=1, # temperature (dimensionless)
type_LTC='PSD',
n_PSD=max_terms - 1,
type_PSD='N-1/N')
s = corr_dict['s'].toarray()
a = corr_dict['a'].toarray()
gamma = corr_dict['gamma'].toarray()
delta = 0
omega_1 = 0.05
omega_2 = 0.02
H = np.array([[omega_1, omega_2], [omega_2, 0]])
V = np.array([[0, 0], [0, 1]])
corr = Correlation(k_max=max_terms, beta=1)
corr.symm_coeff = np.diag(s)
corr.asymm_coeff = np.diag(a)
corr.exp_coeff = np.diag(gamma)
corr.delta_coeff = delta
corr.print()
heom = Hierachy([max_tier] * max_terms, H, V, corr)
rho_0 = np.zeros((2, 2))
rho_0[0, 0] = 1
root = tensor_tree_template(rho_0, [max_tier] * max_terms,
rank=max_tier // 2)
solver = MultiLayer(root, heom.diff(), use_str_name=True)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.max_ode_steps = 100000
dat = []
for n, (time,
r) in enumerate(solver.propagator(
steps=20000,
ode_inter=0.01,
)):
if n % 100 == 0:
head = root.array
print(head.shape)
rho = Tensor.partial_product(r.array, 0, r[0][0].array, 0)
rho = np.reshape(rho, (-1, 4))
flat_data = [time] + list(rho[0])
dat.append(flat_data)
print("Time: {} | Pop 0: {} | Total: {}".format(
flat_data[0], flat_data[1], flat_data[1] + flat_data[-1]))
return np.array(dat)
n_state = 2
omega_1 = np.sqrt(omega_0**2 - zeta**2 * 0.25)
H = np.array([[omega_1, 0.0], [0.0, 0.0]])
V = np.array([[0.0, 1.0], [1.0, 0.0]])
# init state
rho_0 = np.zeros((n_state, n_state))
rho_0[0, 0] = 1
dt_unit = 0.001
callback_interval = 100
count = 50000
# Type settings
max_terms = 3
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.diag(corr_dict['s'].toarray())
corr.asymm_coeff = np.diag(corr_dict['a'].toarray())
corr.exp_coeff = np.diag(corr_dict['gamma'].toarray())
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
def test_brownian(fname=None):
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
root = simple_heom(rho_0, n_dims)
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}