def correlation_es(H, rho0, tlist, taulist, c_op_list, a_op, b_op):
"""
Internal function for calculating correlation functions using the
exponential series solver. See :func:`correlation` usage.
"""
# contruct the Liouvillian
L = liouvillian(H, c_op_list)
if rho0 == None:
rho0 = steady(L)
C_mat = zeros([size(tlist),size(taulist)],dtype=complex)
solES_t = ode2es(L, rho0)
for t_idx in range(len(tlist)):
rho_t = esval_op(solES_t, [tlist[t_idx]])
solES_tau = ode2es(L, b_op * rho_t)
C_mat[t_idx, :] = esval(expect(a_op, solES_tau), taulist)
return C_mat
def correlation_es(H, rho0, tlist, taulist, c_op_list, a_op, b_op):
"""
Internal function for calculating correlation functions using the
exponential series solver. See :func:`correlation` usage.
"""
# contruct the Liouvillian
L = liouvillian(H, c_op_list)
if rho0 == None:
rho0 = steady(L)
C_mat = zeros([size(tlist), size(taulist)], dtype=complex)
solES_t = ode2es(L, rho0)
for t_idx in range(len(tlist)):
rho_t = esval_op(solES_t, [tlist[t_idx]])
solES_tau = ode2es(L, b_op * rho_t)
C_mat[t_idx, :] = esval(expect(a_op, solES_tau), taulist)
return C_mat
def spectrum_ss(H, wlist, c_op_list, a_op, b_op):
"""
Calculate the spectrum corresponding to a correlation function
:math:`\left<A(\\tau)B(0)\\right>`, i.e., the Fourier transform of the
correlation function:
.. math::
S(\omega) = \int_{-\infty}^{\infty} \left<A(\\tau)B(0)\\right> e^{-i\omega\\tau} d\\tau.
Parameters
----------
H : :class:`qutip.Qobj`
system Hamiltonian.
wlist : *list* / *array*
list of frequencies for :math:`\\omega`.
c_op_list : list of :class:`qutip.Qobj`
list of collapse operators.
a_op : :class:`qutip.Qobj`
operator A.
b_op : :class:`qutip.Qobj`
operator B.
Returns
-------
spectrum: *array*
An *array* with spectrum :math:`S(\omega)` for the frequencies specified
in `wlist`.
"""
# contruct the Liouvillian
L = liouvillian(H, c_op_list)
# find the steady state density matrix and a_op and b_op expecation values
rho0 = steady(L)
a_op_ss = expect(a_op, rho0)
b_op_ss = expect(b_op, rho0)
# eseries solution for (b * rho0)(t)
es = ode2es(L, b_op * rho0)
# correlation
corr_es = expect(a_op, es)
# covarience
cov_es = corr_es - real(conjugate(a_op_ss) * b_op_ss)
# spectrum
spectrum = esspec(cov_es, wlist)
return spectrum
def spectrum_ss(H, wlist, c_op_list, a_op, b_op):
"""
Calculate the spectrum corresponding to a correlation function
:math:`\left<A(\\tau)B(0)\\right>`, i.e., the Fourier transform of the
correlation function:
.. math::
S(\omega) = \int_{-\infty}^{\infty} \left<A(\\tau)B(0)\\right> e^{-i\omega\\tau} d\\tau.
Parameters
----------
H : :class:`qutip.Qobj`
system Hamiltonian.
wlist : *list* / *array*
list of frequencies for :math:`\\omega`.
c_op_list : list of :class:`qutip.Qobj`
list of collapse operators.
a_op : :class:`qutip.Qobj`
operator A.
b_op : :class:`qutip.Qobj`
operator B.
Returns
-------
spectrum: *array*
An *array* with spectrum :math:`S(\omega)` for the frequencies specified
in `wlist`.
"""
# contruct the Liouvillian
L = liouvillian(H, c_op_list)
# find the steady state density matrix and a_op and b_op expecation values
rho0 = steady(L)
a_op_ss = expect(a_op, rho0)
b_op_ss = expect(b_op, rho0)
# eseries solution for (b * rho0)(t)
es = ode2es(L, b_op * rho0)
# correlation
corr_es = expect(a_op, es)
# covarience
cov_es = corr_es - real(conjugate(a_op_ss) * b_op_ss)
# spectrum
spectrum = esspec(cov_es, wlist)
return spectrum
def correlation_ss_ode(H, tlist, c_op_list, a_op, b_op, rho0=None):
"""
Internal function for calculating correlation functions using the master
equation solver. See :func:`correlation_ss` usage.
"""
L = liouvillian(H, c_op_list)
if rho0 == None:
rho0 = steady(L)
return mesolve(H, b_op * rho0, tlist, c_op_list, [a_op]).expect[0]
def correlation_ss_ode(H, tlist, c_op_list, a_op, b_op, rho0=None):
"""
Internal function for calculating correlation functions using the master
equation solver. See :func:`correlation_ss` usage.
"""
L = liouvillian(H, c_op_list)
if rho0 == None:
rho0 = steady(L)
return mesolve(H, b_op * rho0, tlist, c_op_list, [a_op]).expect[0]
def correlation_ss_es(H, tlist, c_op_list, a_op, b_op, rho0=None):
"""
Internal function for calculating correlation functions using the
exponential series solver. See :func:`correlation_ss` usage.
"""
# contruct the Liouvillian
L = liouvillian(H, c_op_list)
# find the steady state
if rho0 == None:
rho0 = steady(L)
# evaluate the correlation function
solC_tau = ode2es(L, b_op * rho0)
return esval(expect(a_op, solC_tau), tlist)
def correlation_ss_es(H, tlist, c_op_list, a_op, b_op, rho0=None):
"""
Internal function for calculating correlation functions using the
exponential series solver. See :func:`correlation_ss` usage.
"""
# contruct the Liouvillian
L = liouvillian(H, c_op_list)
# find the steady state
if rho0 == None:
rho0 = steady(L)
# evaluate the correlation function
solC_tau = ode2es(L, b_op * rho0)
return esval(expect(a_op, solC_tau), tlist)
