def floquet_modes_table(f_modes_0, f_energies, tlist, H, T, args=None):
"""
Pre-calculate the Floquet modes for a range of times spanning the floquet
period. Can later be used as a table to look up the floquet modes for
any time.
Parameters
----------
f_modes_0 : list of :class:`qutip.Qobj` (kets)
Floquet modes at :math:`t`
f_energies : list
Floquet energies.
tlist : array
The list of times at which to evaluate the floquet modes.
H : :class:`qutip.Qobj`
system Hamiltonian, time-dependent with period `T`
T : float
The period of the time-dependence of the hamiltonian.
args : dictionary
dictionary with variables required to evaluate H
Returns
-------
output : nested list
A nested list of Floquet modes as kets for each time in `tlist`
"""
# truncate tlist to the driving period
tlist_period = tlist[np.where(tlist <= T)]
f_modes_table_t = [[] for t in tlist_period]
opt = Odeoptions()
opt.rhs_reuse = True
for n, f_mode in enumerate(f_modes_0):
output = mesolve(H, f_mode, tlist_period, [], [], args, opt)
for t_idx, f_state_t in enumerate(output.states):
f_modes_table_t[t_idx].append(
f_state_t * exp(1j * f_energies[n] * tlist_period[t_idx]))
return f_modes_table_t
def floquet_modes_table(f_modes_0, f_energies, tlist, H, T, args=None):
"""
Pre-calculate the Floquet modes for a range of times spanning the floquet
period. Can later be used as a table to look up the floquet modes for
any time.
Parameters
----------
f_modes_0 : list of :class:`qutip.Qobj` (kets)
Floquet modes at :math:`t`
f_energies : list
Floquet energies.
tlist : array
The list of times at which to evaluate the floquet modes.
H : :class:`qutip.Qobj`
system Hamiltonian, time-dependent with period `T`
T : float
The period of the time-dependence of the hamiltonian.
args : dictionary
dictionary with variables required to evaluate H
Returns
-------
output : nested list
A nested list of Floquet modes as kets for each time in `tlist`
"""
# truncate tlist to the driving period
tlist_period = tlist[np.where(tlist <= T)]
f_modes_table_t = [[] for t in tlist_period]
opt = Odeoptions()
opt.rhs_reuse = True
for n, f_mode in enumerate(f_modes_0):
output = mesolve(H, f_mode, tlist_period, [], [], args, opt)
for t_idx, f_state_t in enumerate(output.states):
f_modes_table_t[t_idx].append(f_state_t * exp(1j * f_energies[n]*tlist_period[t_idx]))
return f_modes_table_t
def floquet_modes_table(f_modes_0, f_energies, tlist, H, T, args=None):
"""
Pre-calculate the Floquet modes for a range of times spanning the floquet
period. Can later be used as a table to look up the floquet modes for
any time.
"""
# truncate tlist to the driving period
tlist_period = tlist[where(tlist <= T)]
f_modes_table_t = [[] for t in tlist_period]
opt = Odeoptions()
opt.rhs_reuse = True
for n, f_mode in enumerate(f_modes_0):
output = mesolve(H, f_mode, tlist_period, [], [], args, opt)
for t_idx, f_state_t in enumerate(output.states):
f_modes_table_t[t_idx].append(f_state_t * exp(1j * f_energies[n]*tlist_period[t_idx]))
return f_modes_table_t
def floquet_modes_table(f_modes_0, f_energies, tlist, H, T, args=None):
"""
Pre-calculate the Floquet modes for a range of times spanning the floquet
period. Can later be used as a table to look up the floquet modes for
any time.
"""
# truncate tlist to the driving period
tlist_period = tlist[where(tlist <= T)]
f_modes_table_t = [[] for t in tlist_period]
opt = Odeoptions()
opt.rhs_reuse = True
for n, f_mode in enumerate(f_modes_0):
output = mesolve(H, f_mode, tlist_period, [], [], args, opt)
for t_idx, f_state_t in enumerate(output.states):
f_modes_table_t[t_idx].append(
f_state_t * exp(1j * f_energies[n] * tlist_period[t_idx]))
return f_modes_table_t
def propagator(H, t, c_op_list, H_args=None, opt=None):
"""
Calculate the propagator U(t) for the density matrix or wave function such that
:math:`\psi(t) = U(t)\psi(0)` or :math:`\\rho_{\mathrm vec}(t) = U(t) \\rho_{\mathrm vec}(0)`
where :math:`\\rho_{\mathrm vec}` is the vector representation of the density matrix.
Parameters
----------
H : qobj
Hamiltonian
t : float
Time.
c_op_list : list
List of qobj collapse operators.
Other Parameters
----------------
H_args : list/array/dictionary
Parameters to callback functions for time-dependent Hamiltonians.
Returns
-------
a : qobj
Instance representing the propagator :math:`U(t)`.
"""
if opt == None:
opt = Odeoptions()
opt.rhs_reuse = True
if len(c_op_list) == 0:
# calculate propagator for the wave function
if isinstance(H, FunctionType):
H0 = H(0.0, H_args)
N = H0.shape[0]
elif isinstance(H, list):
if isinstance(H[0], list):
H0 = H[0][0]
N = H0.shape[0]
else:
H0 = H[0]
N = H0.shape[0]
else:
N = H.shape[0]
u = zeros([N, N], dtype=complex)
for n in range(0, N):
psi0 = basis(N, n)
output = mesolve(H, psi0, [0, t], [], [], H_args, opt)
u[:,n] = output.states[1].full().T
# todo: evolving a batch of wave functions:
#psi_0_list = [basis(N, n) for n in range(N)]
#psi_t_list = mesolve(H, psi_0_list, [0, t], [], [], H_args, opt)
#for n in range(0, N):
# u[:,n] = psi_t_list[n][1].full().T
else:
# calculate the propagator for the vector representation of the
# density matrix
if isinstance(H, FunctionType):
H0 = H(0.0, H_args)
N = H0.shape[0]
elif isinstance(H, list):
if isinstance(H[0], list):
H0 = H[0][0]
N = H0.shape[0]
else:
H0 = H[0]
N = H0.shape[0]
else:
N = H.shape[0]
u = zeros([N*N, N*N], dtype=complex)
for n in range(0, N*N):
psi0 = basis(N*N, n)
rho0 = Qobj(vec2mat(psi0.full()))
output = mesolve(H, rho0, [0, t], c_op_list, [], H_args, opt)
u[:,n] = mat2vec(output.states[1].full()).T
return Qobj(u)
def propagator(H, t, c_op_list, H_args=None, opt=None):
"""
Calculate the propagator U(t) for the density matrix or wave function such
that :math:`\psi(t) = U(t)\psi(0)` or
:math:`\\rho_{\mathrm vec}(t) = U(t) \\rho_{\mathrm vec}(0)`
where :math:`\\rho_{\mathrm vec}` is the vector representation of the
density matrix.
Parameters
----------
H : qobj or list
Hamiltonian as a Qobj instance of a nested list of Qobjs and
coefficients in the list-string or list-function format for
time-dependent Hamiltonians (see description in :func:`qutip.mesolve`).
t : float or array-like
Time or list of times for which to evaluate the propagator.
c_op_list : list
List of qobj collapse operators.
H_args : list/array/dictionary
Parameters to callback functions for time-dependent Hamiltonians.
Returns
-------
a : qobj
Instance representing the propagator :math:`U(t)`.
"""
if opt == None:
opt = Odeoptions()
opt.rhs_reuse = True
tlist = [0, t] if isinstance(t,(int,float,np.int64,np.float64)) else t
if len(c_op_list) == 0:
# calculate propagator for the wave function
if isinstance(H, types.FunctionType):
H0 = H(0.0, H_args)
N = H0.shape[0]
elif isinstance(H, list):
if isinstance(H[0], list):
H0 = H[0][0]
N = H0.shape[0]
else:
H0 = H[0]
N = H0.shape[0]
else:
N = H.shape[0]
u = np.zeros([N, N, len(tlist)], dtype=complex)
for n in range(0, N):
psi0 = basis(N, n)
output = mesolve(H, psi0, tlist, [], [], H_args, opt)
for k, t in enumerate(tlist):
u[:,n,k] = output.states[k].full().T
# todo: evolving a batch of wave functions:
#psi_0_list = [basis(N, n) for n in range(N)]
#psi_t_list = mesolve(H, psi_0_list, [0, t], [], [], H_args, opt)
#for n in range(0, N):
# u[:,n] = psi_t_list[n][1].full().T
else:
# calculate the propagator for the vector representation of the
# density matrix
if isinstance(H, types.FunctionType):
H0 = H(0.0, H_args)
N = H0.shape[0]
elif isinstance(H, list):
if isinstance(H[0], list):
H0 = H[0][0]
N = H0.shape[0]
else:
H0 = H[0]
N = H0.shape[0]
else:
N = H.shape[0]
u = np.zeros([N*N, N*N, len(tlist)], dtype=complex)
for n in range(0, N*N):
psi0 = basis(N*N, n)
rho0 = Qobj(vec2mat(psi0.full()))
output = mesolve(H, rho0, tlist, c_op_list, [], H_args, opt)
for k, t in enumerate(tlist):
u[:,n,k] = mat2vec(output.states[k].full()).T
if len(tlist) == 2:
return Qobj(u[:,:,1])
else:
return [Qobj(u[:,:,k]) for k in range(len(tlist))]
def propagator(H, t, c_op_list, H_args=None, opt=None):
"""
Calculate the propagator U(t) for the density matrix or wave function such that
:math:`\psi(t) = U(t)\psi(0)` or :math:`\\rho_{\mathrm vec}(t) = U(t) \\rho_{\mathrm vec}(0)`
where :math:`\\rho_{\mathrm vec}` is the vector representation of the density matrix.
Parameters
----------
H : qobj
Hamiltonian
t : float
Time.
c_op_list : list
List of qobj collapse operators.
Other Parameters
----------------
H_args : list/array/dictionary
Parameters to callback functions for time-dependent Hamiltonians.
Returns
-------
a : qobj
Instance representing the propagator :math:`U(t)`.
"""
if opt == None:
opt = Odeoptions()
opt.rhs_reuse = True
if len(c_op_list) == 0:
# calculate propagator for the wave function
if isinstance(H, FunctionType):
H0 = H(0.0, H_args)
N = H0.shape[0]
elif isinstance(H, list):
if isinstance(H[0], list):
H0 = H[0][0]
N = H0.shape[0]
else:
H0 = H[0]
N = H0.shape[0]
else:
N = H.shape[0]
u = zeros([N, N], dtype=complex)
for n in range(0, N):
psi0 = basis(N, n)
output = mesolve(H, psi0, [0, t], [], [], H_args, opt)
u[:, n] = output.states[1].full().T
# todo: evolving a batch of wave functions:
#psi_0_list = [basis(N, n) for n in range(N)]
#psi_t_list = mesolve(H, psi_0_list, [0, t], [], [], H_args, opt)
#for n in range(0, N):
# u[:,n] = psi_t_list[n][1].full().T
else:
# calculate the propagator for the vector representation of the
# density matrix
if isinstance(H, FunctionType):
H0 = H(0.0, H_args)
N = H0.shape[0]
elif isinstance(H, list):
if isinstance(H[0], list):
H0 = H[0][0]
N = H0.shape[0]
else:
H0 = H[0]
N = H0.shape[0]
else:
N = H.shape[0]
u = zeros([N * N, N * N], dtype=complex)
for n in range(0, N * N):
psi0 = basis(N * N, n)
rho0 = Qobj(vec2mat(psi0.full()))
output = mesolve(H, rho0, [0, t], c_op_list, [], H_args, opt)
u[:, n] = mat2vec(output.states[1].full()).T
return Qobj(u)
