def tensor_tree_template(init_rho, pb_index, rank=1, nbranch=2):
"""Get rho_n from rho in a Tensor Tree representation.
Parameters
----------
rho : np.ndarray
"""
n_state = get_n_state(init_rho)
n_vec = np.zeros((rank, ), dtype=DTYPE)
n_vec[0] = 1.0
root_array = np.tensordot(init_rho, n_vec, axes=0)
max_terms = len(pb_index)
for i in pb_index:
assert rank <= i
# generate leaves
leaves = list(range(max_terms))
class new_spf(object):
counter = 0
prefix = 'SPF'
def __new__(cls):
name = cls.prefix + str(cls.counter)
cls.counter += 1
return name
importance = list(reversed(range(len(pb_index))))
graph, spf_root = huffman_tree(
leaves,
importances=importance,
obj_new=new_spf,
n_branch=nbranch,
)
root = 'root'
graph[root] = [str(max_terms), str(max_terms + 1), spf_root]
print(graph, root)
root = Tensor.generate(graph, root)
root.set_array(root_array)
bond_dict = {}
# Leaves
l_range = list(pb_index) + [n_state] * 2
for s, i, t, j in root.linkage_visitor():
if isinstance(t, Leaf):
bond_dict[(s, i, t, j)] = l_range[int(t.name)]
else:
bond_dict[(s, i, t, j)] = rank
autocomplete(root, bond_dict)
return root
def sbm_zt(including_bath=False, split=False, snd=False):
sbm_para_dict = {
'including_bath':
including_bath,
'e1':
0.,
'e2':
Quantity(6500, 'cm-1').value_in_au,
'v':
Quantity(500, 'cm-1').value_in_au,
"omega_list": [
Quantity(2100, 'cm-1').value_in_au,
Quantity(650, 'cm-1').value_in_au,
Quantity(400, 'cm-1').value_in_au,
Quantity(150, 'cm-1').value_in_au
],
'lambda_list': ([Quantity(750, 'cm-1').value_in_au] * 4),
'dim_list': [10, 14, 20, 30],
'stop':
Quantity(3 * 2250, 'cm-1').value_in_au,
'n':
32,
'dim':
30,
'lambda_g':
Quantity(2250, 'cm-1').value_in_au,
'omega_g':
Quantity(500, 'cm-1').value_in_au,
'lambda_d':
Quantity(1250, 'cm-1').value_in_au,
'omega_d':
Quantity(50, 'cm-1').value_in_au,
'mu':
Quantity(250, 'cm-1').value_in_au,
'tau':
Quantity(30, 'fs').value_in_au,
't_d':
Quantity(60, 'fs').value_in_au,
'omega':
Quantity(13000, 'cm-1').value_in_au,
}
sbm = SpinBosonModel(**sbm_para_dict)
# Define the topological structure of the ML-MCTDH tree
graph, root = sbm.autograph(n_branch=2)
root = Tensor.generate(graph, root)
# Define the detailed parameters for the MC-MCTDH tree
solver = MultiLayer(root, sbm.h_list, f_list=sbm.f_list, use_str_name=True)
bond_dict = {}
# Leaves
for s, i, t, j in root.linkage_visitor():
if isinstance(t, Leaf):
bond_dict[(s, i, t, j)] = sbm.dimensions[t.name]
# ELEC part
elec_r = root[0][0]
for s, i, t, j in elec_r.linkage_visitor(leaf=False):
raise NotImplementedError()
# INNER part
inner_r = root[1][0] if including_bath else root
if including_bath:
bond_dict[(root, 1, inner_r, 0)] = 60
for s, i, t, j in inner_r.linkage_visitor(leaf=False):
bond_dict[(s, i, t, j)] = 50
# OUTER part
if including_bath:
outer_r = root[2][0]
bond_dict[(root, 2, outer_r, 0)] = 20
for s, i, t, j in root[2][0].linkage_visitor(leaf=False):
bond_dict[(s, i, t, j)] = 10
solver.autocomplete(bond_dict, max_entangled=False)
# Define the computation details
solver.settings(
max_ode_steps=100,
cmf_steps=(1 if split else 10),
ode_method='RK45',
ps_method='s',
snd_order=snd,
)
root.is_normalized = True
# Define the obersevable of interest
projector = np.array([[0., 0.], [0., 1.]])
op = [[[root[0][0], projector]]]
t_p = []
for time, _ in solver.propagator(
steps=20,
ode_inter=Quantity(0.2, 'fs').value_in_au,
split=split,
move_energy=True,
):
t, p = (Quantity(time).convert_to(unit='fs').value,
solver.expection(op=op))
t_p.append((t, p))
logging.warning('Time: {:.2f} fs, P2: {}'.format(t, p))
if np.abs(p) > 0.5:
break
# Save the results
msg = 'split' if split else 'origin'
msg2 = 'snd' if snd else 'fst'
np.savetxt('sbm-zt-{}-{}.dat'.format(msg, msg2), t_p)
def sbm_ft(including_bath=False, snd=False):
# Define parameters of the model.
sbm = SpinBosonModel(
including_bath=including_bath,
e1=0.,
e2=Quantity(6500, 'cm-1').value_in_au,
v=Quantity(500, 'cm-1').value_in_au,
omega_list=[Quantity(2100, 'cm-1').value_in_au],
lambda_list=([Quantity(750, 'cm-1').value_in_au]),
dim_list=[10],
stop=Quantity(10000, 'cm-1').value_in_au,
n=32,
dim=30,
lambda_g=Quantity(2250, 'cm-1').value_in_au,
omega_g=Quantity(500, 'cm-1').value_in_au,
lambda_d=Quantity(1250, 'cm-1').value_in_au,
omega_d=Quantity(50, 'cm-1').value_in_au,
mu=Quantity(250, 'cm-1').value_in_au,
tau=Quantity(3, 'fs').value_in_au,
t_d=Quantity(6, 'fs').value_in_au,
omega=Quantity(13000, 'cm-1').value_in_au,
)
# Define the topological structure of the ML-MCTDH tree
graph, root = {
'ROOT': ['ELECs', 'I0s'],
'ELECs': ['ELEC', "ELEC'"],
'I0s': ['I0', "I0'"],
}, 'ROOT'
root = Tensor.generate(graph, root)
# Define the detailed parameters for the MC-MCTDH tree
solver = MultiLayer(root, sbm.h_list, f_list=sbm.f_list, use_str_name=True)
bond_dict = {}
# Leaves
for s, i, t, j in root.linkage_visitor():
if isinstance(t, Leaf):
try:
dim = sbm.dimensions[t.name]
except KeyError:
dim = sbm.dimensions[t.name[:-1]]
bond_dict[(s, i, t, j)] = dim
s_ax = s.axis
p, p_ax = s[s_ax]
bond_dict[(p, p_ax, s, s_ax)] = dim**2 if dim < 9 else 50
solver.autocomplete(bond_dict, max_entangled=True)
# Define the computation details
solver.settings(cmf_steps=10,
ode_method='RK45',
ps_method='split-unite',
snd_order=snd)
logging.info("Size of a wfn: {} complexes".format(len(root.vectorize())))
# Do the imaginary time propogation
inv_tem = 1 / 1000
steps = 100
for time, _ in solver.propagator(
steps=steps,
ode_inter=Quantity(inv_tem / steps / 2, unit='K-1').value_in_au,
split=True,
imaginary=True):
t = 2 * Quantity(time).convert_to(unit='K-1').value
z = solver.relative_partition_function
kelvin = 'inf' if abs(t) < 1.e-14 else 1.0 / t
logging.warning('Temperatue: {} K; ln(Z/Z_0): {}'.format(
kelvin, np.log(z)))
# Define the obersevable of interest
projector = np.array([[0., 0.], [0., 1.]])
op = [[[root[0][0][1][0], projector]]]
# Do the real time propogation
tp_list = []
steps = 100
root.is_normalized = True
for time, _ in solver.propagator(steps=steps,
ode_inter=Quantity(10 / steps,
'fs').value_in_au,
split=True,
imaginary=False):
t = Quantity(time).convert_to(unit='fs').value
p = solver.expection(op=op)
logging.warning('Time: {:.2f} fs; P2: {}'.format(t, p))
tp_list.append((t, p))
return np.array(tp_list)
def sbm_zt(including_bath=False, split=False, snd=False):
omega = 13000
sbm = SpinBosonModel(
including_bath=including_bath,
e1=0.,
e2=Quantity(6500, 'cm-1').value_in_au,
v=Quantity(500, 'cm-1').value_in_au,
omega_list=[
Quantity(2100, 'cm-1').value_in_au,
Quantity(650, 'cm-1').value_in_au,
Quantity(400, 'cm-1').value_in_au,
Quantity(150, 'cm-1').value_in_au
],
lambda_list=([Quantity(750, 'cm-1').value_in_au] * 4),
dim_list=[10, 14, 20, 30],
stop=Quantity(3 * 2250, 'cm-1').value_in_au,
n=32,
dim=30,
lambda_g=Quantity(2250, 'cm-1').value_in_au,
omega_g=Quantity(500, 'cm-1').value_in_au,
lambda_d=Quantity(1250, 'cm-1').value_in_au,
omega_d=Quantity(50, 'cm-1').value_in_au,
mu=Quantity(250, 'cm-1').value_in_au,
tau=Quantity(30, 'fs').value_in_au,
t_d=Quantity(60, 'fs').value_in_au,
omega=Quantity(omega, 'cm-1').value_in_au,
)
# Define the topological structure of the ML-MCTDH tree
graph, root = sbm.autograph(n_branch=2)
root = Tensor.generate(graph, root)
# Define the detailed parameters for the MC-MCTDH tree
solver = MultiLayer(root, sbm.h_list, f_list=sbm.f_list, use_str_name=True)
bond_dict = {}
# Leaves
for s, i, t, j in root.linkage_visitor():
if isinstance(t, Leaf):
bond_dict[(s, i, t, j)] = sbm.dimensions[t.name]
# ELEC part
elec_r = root[0][0]
for s, i, t, j in elec_r.linkage_visitor(leaf=False):
raise NotImplementedError()
# INNER part
inner_r = root[1][0] if including_bath else root
if including_bath:
bond_dict[(root, 1, inner_r, 0)] = 60
for s, i, t, j in inner_r.linkage_visitor(leaf=False):
bond_dict[(s, i, t, j)] = 50
# OUTER part
if including_bath:
outer_r = root[2][0]
bond_dict[(root, 2, outer_r, 0)] = 20
for s, i, t, j in root[2][0].linkage_visitor(leaf=False):
bond_dict[(s, i, t, j)] = 10
solver.autocomplete(bond_dict, max_entangled=False)
# Define the computation details
solver.settings(
max_ode_steps=100,
cmf_steps=(1 if split else 10),
ode_method='RK45',
ps_method='s',
snd_order=snd,
)
print("Size of a wfn: {} complexes".format(len(root.vectorize())))
root.is_normalized = True
# Define the obersevable of interest
projector = np.array([[0., 0.], [0., 1.]])
op = [[[root[0][0], projector]]]
t_p = []
for time, _ in solver.propagator(
steps=20,
ode_inter=Quantity(0.2, 'fs').value_in_au,
split=split,
move_energy=True,
):
t, p = (Quantity(time).convert_to(unit='fs').value,
solver.expection(op=op))
t_p.append((t, p))
logging.warning('Time: {:.2f} fs, P2: {}'.format(t, p))
if np.abs(p) > 0.5:
break
return np.array(t_p)
