def absorption(self, e_min, e_max, de, rho_0, t_final, dt,
dipole_file='dipole_dipole.dat',
is_damped=False):
utils.print_banner("CALCULATING LINEAR ABSORPTION SPECTRUM")
energies = np.arange(e_min, e_max, de)
omegas = energies/const.hbar
mu = self.dipole_site
mu_rho_0 = np.dot(mu, rho_0)
times, mu_rho, x = self.dynamics.propagate(mu_rho_0, 0.0, t_final, dt)
Cw = np.zeros(len(omegas))
fdipole = open(dipole_file,'w')
t_damp = 0.
expi = np.exp(1j*np.outer(omegas,times))
for t, time in enumerate(times):
weight = dt - 0.5*dt*(t==0 or t==len(times)-1)
Ct = np.trace(np.dot(mu,mu_rho[t]))
if is_damped and t > t_damp:
Ct *= switch_to_zero(time,t_damp,t_final)
fdipole.write('%0.6f %0.6f %0.6f\n'%(
time, Ct.real, Ct.imag))
Cw += weight*(expi[:,t]*Ct).real
fdipole.close()
return energies, Cw
def __init__(self,
hamiltonian,
method='Redfield',
is_secular=False,
is_verbose=False):
"""Initialize the Redfield class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
method : str
The weak-coupling method, either 'Redfield', 'TCL2', or 'TC2'.
is_secular : bool
Flag to indicate the secular approximation.
"""
assert (method in ['Redfield', 'TCL2', 'TC2'])
if is_verbose:
utils.print_banner("PERFORMING RDM DYNAMICS WITH METHOD = %s" %
(method))
self.ham = hamiltonian
self.method = method
self.is_secular = is_secular
self.is_verbose = is_verbose
self.setup()
def __init__(self, hamiltonian, is_verbose=True):
"""Initialize the Unitary evolution class.
Parameters
----------
hamiltonian : HamiltonianSystem
An instance of the pyrho HamiltonianSystem class.
"""
if is_verbose:
utils.print_banner("PERFORMING UNITARY DYNAMICS")
self.ham = hamiltonian
def __init__(self, hamiltonian, is_verbose=True):
"""Initialize the Unitary evolution class.
Parameters
----------
hamiltonian : HamiltonianSystem
An instance of the pyrho HamiltonianSystem class.
"""
if is_verbose:
utils.print_banner("PERFORMING UNITARY DYNAMICS")
self.ham = hamiltonian
def __init__(self,
hamiltonian,
L=1,
K=0,
K_truncation='Ishizaki-Tanimura',
L_truncation='TNL',
is_scaled=True):
"""Initialize the HEOM class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
L : int
The "hierarchy depth."
L_truncation: str
Hierarchy closure type (time-local or time-nonlocal)
K : int
The Matsubara truncation.
K_truncation : str
The Matsubara truncation type (or terminator).
is_scaled : bool
Flag to use scaled ADMs, which are useful for filtering.
"""
assert (K_truncation in ['None', 'Ishizaki-Tanimura'])
assert (L_truncation in ['TNL', 'TL'])
utils.print_banner("PERFORMING RDM DYNAMICS WITH "
"THE HIERARCHICAL EQUATIONS OF MOTION")
self.ham = hamiltonian
self.Lmax = L
self.Kmax = K
self.is_scaled = is_scaled
self.L_truncation = L_truncation
self.K_truncation = K_truncation
print "--- Hierarchy depth, L =", self.Lmax
print "--- Using hierarchy closure:", self.L_truncation
print "--- Maximum Matsubara frequency, K =", self.Kmax
print "--- Using Matsubara truncation scheme:", self.K_truncation
# TODO(TCB): Implement filtering.
# Scaling makes no difference unless using tolerant filtering
if self.is_scaled:
print "--- Using Shi et al. scaled ADMs."
else:
print "--- Using original *unscaled* ADMs."
self.initialize_hierarchy_nmats()
self.precompute_matsubara()
def __init__(self,
ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=1,
is_verbose=True,
sample_wigner=False):
"""Initialize the Hamiltonian class.
Parameters
----------
ham_sys : np.array
The system Hamiltonian in the site basis.
ham_sysbath : list of np.arrays
The system part of the system-bath operator for each bath.
spec_densities : list of functions
The spectral density function for each bath.
kT : float
Thermal energy, kT, in chosen units.
hbar : float
Reduced Planck constant, hbar, in chosen units.
"""
# Set these shared constants
const.kT = kT
const.hbar = hbar
if is_verbose:
utils.print_banner("INITIALIZING SYSTEM+BATH HAMILTONIAN")
self.init_system(ham_sys, is_verbose)
self.sample_wigner = sample_wigner
self.sysbath = ham_sysbath
self.spec_densities = spec_densities
assert len(ham_sysbath) == len(spec_densities)
self.nbath = len(ham_sysbath)
# 'sd' is a list of 'SpecDens' instances that have member
# variables lamda, omega_c and member function J(omega)
self.sd = []
self.coupling = []
n = 0
for spec_dens in self.spec_densities:
self.sd.append(SpecDens(spec_dens))
self.sd[n].write_Jw('Jw%d.dat' % (n))
n += 1
def __init__(self, hamiltonian, dynamics_slow, dynamics_fast, omega_split=None):
"""Initialize the Hybrid class
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
"""
utils.print_banner("PERFORMING RDM DYNAMICS WITH HYBRID METHOD")
self.ham = hamiltonian
self.dynamics_slow = dynamics_slow
self.dynamics_fast = dynamics_fast
self.omega_split = omega_split
self.setup()
def __init__(self, hamiltonian, L=1, K=0,
K_truncation='Ishizaki-Tanimura', L_truncation='TNL'):
"""Initialize the HEOM class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
L : int
The "hierarchy depth."
L_truncation: str
Hierarchy closure type (time-local or time-nonlocal)
K : int
The Matsubara truncation.
K_truncation : str
The Matsubara truncation type (or terminator).
"""
assert(K_truncation in ['None','Ishizaki-Tanimura'])
assert(L_truncation in ['TNL','TL'])
utils.print_banner("PERFORMING RDM DYNAMICS WITH "
"THE HIERARCHICAL EQUATIONS OF MOTION")
self.ham = hamiltonian
self.Lmax = L
self.Kmax = K
self.Nk = K+1
self.L_truncation = L_truncation
self.K_truncation = K_truncation
print("--- Hierarchy depth, L =", self.Lmax)
print("--- Using hierarchy closure:", self.L_truncation)
print("--- Maximum Matsubara frequency, K =", self.Kmax)
print("--- Using Matsubara truncation scheme:", self.K_truncation)
if self.ham.sd[0].sd_type == 'ohmic-exp':
self.nlorentz = 3 # number of Lorenztians to fit
elif self.ham.sd[0].sd_type == 'cubic-exp':
self.nlorentz = 4 # number of Lorenztians to fit
elif self.ham.sd[0].sd_type == 'custom':
self.nlorentz = len(self.ham.sd[0].pks) # number of Lorenztians as input
else:
self.nlorentz = 0
self.initialize_hierarchy_nmats()
self.precompute_matsubara()
def __init__(self, hamiltonian, nmode=300, ntraj=100):
"""Initialize the Ehrenfest class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
nmode : int
The number of explicit classical modes
ntraj : int
The number of trajectories over which to average
"""
utils.print_banner("PERFORMING EHRENFEST DYNAMICS")
self.ham = hamiltonian
self.nmode = nmode
self.ntraj = ntraj
def __init__(self, hamiltonian, nmode=300, ntraj=100):
"""Initialize the Ehrenfest class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
nmode : int
The number of explicit classical modes
ntraj : int
The number of trajectories over which to average
"""
utils.print_banner("PERFORMING EHRENFEST DYNAMICS")
self.ham = hamiltonian
self.nmode = nmode
self.ntraj = ntraj
def __init__(self, hamiltonian, L=1, K=0,
truncation_type='Ishizaki-Tanimura', is_scaled=True):
"""Initialize the HEOM class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
L : int
The "hierarchy depth."
K : int
The Matsubara truncation.
truncation_type : str
The hierarchy truncation type (or terminator).
is_scaled : bool
Flag to use scaled ADMs, which are useful for filtering.
"""
assert(truncation_type in ['None','Ishizaki-Tanimura','TL'])
utils.print_banner("PERFORMING RDM DYNAMICS WITH "
"THE HIERARCHICAL EQUATIONS OF MOTION")
self.ham = hamiltonian
self.Lmax = L
self.Kmax = K
self.is_scaled = is_scaled
self.truncation_type = truncation_type
print "--- Hierarchy depth, L =", self.Lmax
print "--- Maximum Matsubara frequency, K =", self.Kmax
print "--- Using Matsubara truncation scheme:", self.truncation_type
# TODO(TCB): Implement filtering.
# Scaling makes no difference unless using tolerant filtering
if self.is_scaled:
print "--- Using Shi et al. scaled ADMs."
else:
print "--- Using original *unscaled* ADMs."
self.initialize_hierarchy_nmats()
self.precompute_matsubara()
def __init__(self, ham_sys, ham_sysbath, spec_densities, kT, hbar=1, is_verbose=True):
"""Initialize the Hamiltonian class.
Parameters
----------
ham_sys : np.array
The system Hamiltonian in the site basis.
ham_sysbath : list of np.arrays
The system part of the system-bath operator for each bath.
spec_densities : list of functions
The spectral density function for each bath.
kT : float
Thermal energy, kT, in chosen units.
hbar : float
Reduced Planck constant, hbar, in chosen units.
"""
# Set these shared constants
const.kT = kT
const.hbar = hbar
if is_verbose:
utils.print_banner("INITIALIZING SYSTEM+BATH HAMILTONIAN")
self.init_system(ham_sys, is_verbose)
self.sysbath = ham_sysbath
self.spec_densities = spec_densities
assert len(ham_sysbath) == len(spec_densities)
self.nbath = len(ham_sysbath)
# 'sd' is a list of 'SpecDens' instances that have member
# variables lamda, omega_c and member function J(omega)
self.sd = []
n = 0
for spec_dens in self.spec_densities:
self.sd.append(SpecDens(spec_dens))
self.sd[n].write_Jw('Jw%d.dat'%(n))
n += 1
def __init__(self, hamiltonian, method='Redfield', is_secular=False, is_verbose=True):
"""Initialize the Redfield class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
method : str
The weak-coupling method, either 'Redfield', 'TCL2', or 'TC2'.
is_secular : bool
Flag to indicate the secular approximation.
"""
assert(method in ['Redfield', 'TCL2', 'TC2'])
if is_verbose:
utils.print_banner("PERFORMING RDM DYNAMICS WITH METHOD = %s"%(method))
self.ham = hamiltonian
self.method = method
self.is_secular = is_secular
self.is_verbose = is_verbose
self.setup()
def __init__(self,
hamiltonian,
dynamics_slow,
dynamics_fast,
omega_split=None,
use_PD=False):
"""Initialize the Hybrid class
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class.
"""
raise NotImplementedError
utils.print_banner("PERFORMING RDM DYNAMICS WITH HYBRID METHOD")
self.ham = hamiltonian
self.dynamics_slow = dynamics_slow
self.dynamics_fast = dynamics_fast
self.omega_split = omega_split
self.use_PD = use_PD
self.setup()
def absorption(self,
e_min,
e_max,
de,
rho_0,
t_final,
dt,
dipole_file='dipole_dipole.dat',
is_damped=True,
lineshape_func=False):
utils.print_banner("CALCULATING LINEAR ABSORPTION SPECTRUM")
energies = np.arange(e_min, e_max, de)
omegas = energies / const.hbar
mu = self.dipole_site
t_damp = 0.
if lineshape_func == True:
if self.dynamics.ham.nsite == 2:
omega_eg = self.dynamics.ham.omega_diff[1, 0]
times = np.zeros(int(t_final / dt))
for n in range(len(times)):
times[n] = n * dt
Cw = np.zeros(len(omegas))
expi = np.exp(1j * (np.outer(omegas, times)))
for t, time in enumerate(times):
weight = dt - 0.5 * dt * (t == 0 or t == len(times) - 1)
gt = self.dynamics.ham.sd[0].line_func(t * dt)
Ct = np.exp(-1j * omega_eg * t * dt - gt)
if is_damped and t > t_damp:
Ct *= switch_to_zero(time, t_damp, t_final)
Cw += weight * (expi[:, t] * Ct).real
return energies, (mu[1, 0]**2) * Cw
else:
omega_diff = self.dynamics.ham.omega_diff
nbath = self.dynamics.ham.nbath
nsite = self.dynamics.ham.nsite
sys_eig = self.dynamics.ham.site2eig(self.dynamics.ham.sys)
sysbath_eig = []
for n in range(nbath):
sysbath_eig.append(
self.dynamics.ham.site2eig(
self.dynamics.ham.sysbath[n]))
mu_eig = self.dynamics.ham.site2eig(mu)
gs_index = np.where(np.diag(sys_eig) == 0.)[0][0]
markov_rate = []
for l in range(nbath):
markovrate_l = np.zeros((nsite, nsite))
for m in range(nsite):
for n in range(nsite):
markovrate_l[
m, n] = self.dynamics.ham.sd[l].markov_poprate(
omega_diff[n, m])
markovrate_l[n, n] = 0.0
markov_rate.append(markovrate_l)
times = np.zeros(int(t_final / dt))
for n in range(len(times)):
times[n] = n * dt
full_rate = np.zeros((nsite, nsite))
for n in range(nbath):
full_rate += (sysbath_eig[n]**2) * markov_rate[n]
full_rate_sum = np.zeros(nsite)
for n in range(nsite):
full_rate_sum[n] = (np.sum(full_rate[n, :]))
gammas = np.zeros((nsite))
for m in range(nbath):
for n in range(nsite):
gammas[n] += sysbath_eig[m][n, n]**2
t_damp = 0.
times = np.zeros(int(t_final / dt))
for n in range(len(times)):
times[n] = n * dt
expi = np.exp(1j * (np.outer(omegas, times)))
absw = np.zeros(len(omegas))
# Currently assumes all sites have identical J(w); not sure about individual J(w) after site to eig conversion
for n in range(nsite):
Cw = np.zeros(len(omegas))
for t, time in enumerate(times):
weight = dt - 0.5 * dt * (t == 0
or t == len(times) - 1)
gt = self.dynamics.ham.sd[0].line_func(t * dt)
gt0 = self.dynamics.ham.sd[0].line_func(0.)
Ct = np.exp(-1j * omega_diff[n, gs_index] * t * dt -
gammas[n] * (gt - gt0) -
0.5 * full_rate_sum[n])
if is_damped and t > t_damp:
Ct *= switch_to_zero(time, t_damp, t_final)
Cw += weight * (expi[:, t] * Ct).real
absw += (mu_eig[n, gs_index]**2) * Cw
return energies, absw
else:
nbath = self.dynamics.ham.nbath
nsite = self.dynamics.ham.nsite
sysbath_eig = []
for n in range(nbath):
sysbath_eig.append(
self.dynamics.ham.site2eig(self.dynamics.ham.sysbath[n]))
mu_rho_0 = np.dot(mu, rho_0)
times, mu_rho = self.dynamics.propagate(mu_rho_0, 0.0, t_final, dt)
Cw = np.zeros(len(omegas))
fdipole = open(dipole_file, 'w')
t_damp = 0.
expi = np.exp(1j * np.outer(omegas, times))
for t, time in enumerate(times):
weight = dt - 0.5 * dt * (t == 0 or t == len(times) - 1)
Ct = np.trace(np.dot(mu, mu_rho[t]))
if is_damped and t > t_damp:
Ct *= switch_to_zero(time, t_damp, t_final)
fdipole.write('%0.6f %0.6f %0.6f\n' % (time, Ct.real, Ct.imag))
Cw += weight * (expi[:, t] * Ct).real
fdipole.close()
return energies, Cw
def two_dimensional(self, e1_min, e1_max, de1,
e3_min, e3_max, de3,
t2_min, t2_max, dt2,
rho_g, t_final, dt):
utils.print_banner("CALCULATING TWO-DIMENSIONAL SPECTRUM")
energy1s = np.arange(e1_min, e1_max, de1)
energy3s = np.arange(e3_min, e3_max, de3)
omega1s = energy1s/const.hbar
omega3s = energy3s/const.hbar
time2s = np.arange(t2_min, t2_max+1e-8, dt2)
times = np.arange(0.0, t_final, dt)
dt2_over_dt = int(dt2/dt)
spectrum = np.zeros( (len(omega3s),len(time2s),len(omega1s)) )
print "--- Spectrum will require O(%d) propagations."%(len(times)*len(times))
mu_p = np.tril(self.dipole_site)
mu_m = np.triu(self.dipole_site)
mu_rp_ese = [ [mu_m,'R'], [mu_p,'L'], [mu_p,'R'], 1 ] # R2
mu_rp_gsb = [ [mu_m,'R'], [mu_p,'R'], [mu_p,'L'], 1 ] # R3
mu_rp_esa = [ [mu_m,'R'], [mu_p,'L'], [mu_p,'L'], -1 ] # R5
mu_nr_ese = [ [mu_p,'L'], [mu_m,'R'], [mu_p,'R'], 1 ] # R1
mu_nr_gsb = [ [mu_p,'L'], [mu_m,'L'], [mu_p,'L'], 1 ] # R4
mu_nr_esa = [ [mu_p,'L'], [mu_m,'R'], [mu_p,'L'], -1 ] # R6
# This part changes based on the desired spectrum
# e.g. just the ESA of the non-rephasing spectrum:
# mu_rp = []
# mu_nr = [mu_nr_esa]
# Total 2D spectrum:
mu_rp = [mu_rp_ese, mu_rp_gsb, mu_rp_esa]
mu_nr = [mu_nr_ese, mu_nr_gsb, mu_nr_esa]
# This part never changes
mu_ops = [mu_rp, mu_nr]
Rsignal = []
Rsignal.append(np.zeros( (len(times),len(time2s),len(times)), dtype=np.complex_))
Rsignal.append(np.zeros( (len(times),len(time2s),len(times)), dtype=np.complex_))
x, rho_g_baths, x = self.dynamics.propagate(
rho_g, 0.0, 0.0, dt,
input_has_bath=False, output_has_bath=True,
is_verbose=False)
rho_g_bath = rho_g_baths[0]
print "--- Calculating third-order response function ...",
for ph in [0,1]:
for mu_op in mu_ops[ph]:
rho_0 = self.act(mu_op[0],rho_g_bath)
t1s, rhos_t1, x = self.dynamics.propagate(
rho_0, 0.0, t_final, dt,
input_has_bath=True, output_has_bath=True,
is_verbose=False)
for t1 in range(len(times)):
rho_t1 = rhos_t1[t1]
rho_t1_0 = self.act(mu_op[1],rho_t1)
t2s, rhos_t2, x = self.dynamics.propagate(
rho_t1_0, t2_min, t2_max, dt,
input_has_bath=True, output_has_bath=True,
is_verbose=False)
for t2 in range(len(time2s)):
rho_t2 = rhos_t2[t2*dt2_over_dt]
rho_t2_0 = self.act(mu_op[2],rho_t2)
t3s, rhos_t3, x = self.dynamics.propagate(
rho_t2_0, 0.0, t_final, dt,
input_has_bath=True, output_has_bath=False,
is_verbose=False)
for t3 in range(len(times)):
rho_t3 = rhos_t3[t3]
sign = mu_op[3]
Rsignal[ph][t3,t2,t1] += sign*np.trace(np.dot(mu_m,rho_t3))
print "done."
print "--- Performing 2D Fourier transform ...",
for w3, omega3 in enumerate(omega3s):
for w1, omega1 in enumerate(omega1s):
for t1, time1 in enumerate(times):
weight1 = dt - 0.5*dt*(t1==0 or t1==len(times)-1)
exp_iw1t1 = np.exp(1j*omega1*time1)
exp_miw1t1 = exp_iw1t1.conj()
for t3, time3 in enumerate(times):
weight3 = dt - 0.5*dt*(t3==0 or t3==len(times)-1)
exp_iw3t3 = np.exp(1j*omega3*time3)
for t2 in range(len(time2s)):
spectrum[w3,t2,w1] += weight1*weight3*(
exp_iw1t1*exp_iw3t3*Rsignal[1][t3,t2,t1]
+ exp_miw1t1*exp_iw3t3*Rsignal[0][t3,t2,t1] ).real
#np.exp(1j*(omega1*time1+omega3*time3))*Rsignal[1][t3,t2,t1]
#+np.exp(1j*(-omega1*time1+omega3*time3))*Rsignal[0][t3,t2,t1] ).real
print "done."
spectra = []
for t2 in range(len(time2s)):
spectra.append( spectrum[:,t2,:] )
return energy1s, energy3s, time2s, spectra
def two_dimensional(self, e1_min, e1_max, de1,
e3_min, e3_max, de3,
time2_min, time2_max, dt2,
rho_g, time_final, dt, lioupath = 'total', is_damped=True, lineshape_func = False):
utils.print_banner("CALCULATING TWO-DIMENSIONAL SPECTRUM")
if lioupath == 'total':
print '--- Including all Liouville pathways.'
else:
print '--- Including only selected Liouville pathways.'
energy1s = np.arange(e1_min, e1_max, de1)
energy3s = np.arange(e3_min, e3_max, de3)
omega1s = energy1s/const.hbar
omega3s = energy3s/const.hbar
time2_max += 1e-8 # try to include time2_max
time2s = np.arange(time2_min, time2_max, dt2)
times = np.arange(0.0, time_final, dt)
spectrum = np.zeros( (len(omega3s),len(time2s),len(omega1s)) )
print "--- Spectrum will require O(%d) propagations."%(len(times)*len(time2s))
print "--- Calculating third-order response function ...",
try:
Rsignal = []
Rsignal.append(np.zeros( (len(times),len(time2s),len(times)), dtype=np.complex))
Rsignal.append(np.zeros( (len(times),len(time2s),len(times)), dtype=np.complex))
for traj in range(self.dynamics.ntraj):
R_rp, R_nr = self.calculate_R3(rho_g, time2_min, time2_max, dt2, time_final, dt, is_damped=is_damped, lioupath=lioupath, lineshape_func=lineshape_func)
Rsignal[0] += R_rp/self.dynamics.ntraj
Rsignal[1] += R_nr/self.dynamics.ntraj
except AttributeError:
Rsignal = self.calculate_R3(rho_g, time2_min, time2_max, dt2, time_final, dt, is_damped=is_damped, lioupath=lioupath, lineshape_func=lineshape_func)
# print time correlation R3
# for n in range(1,len(times)-1):
# print Rsignal[0][0,0,n].real
print "done."
print "--- Performing 2D Fourier transform ...",
expi1 = np.exp(1j*np.outer(omega1s,times))
expi1[:,0] *= 0.5*dt
expi1[:,1:] *= dt
expi3 = np.exp(1j*np.outer(omega3s,times))
expi3[:,0] *= 0.5*dt
expi3[:,1:] *= dt
spectrum = np.einsum('ws,xu,uts->xtw',expi1,expi3,Rsignal[1]).real
spectrum += np.einsum('ws,xu,uts->xtw',expi1.conj(),expi3,Rsignal[0]).real
# for w3, omega3 in enumerate(omega3s):
# for w1, omega1 in enumerate(omega1s):
# for t1, time1 in enumerate(times):
# weight1 = dt - 0.5*dt*(t1==0 or t1==len(times)-1)
# exp_iw1t1 = np.exp(1j*omega1*time1)
# exp_miw1t1 = exp_iw1t1.conj()
# for t3, time3 in enumerate(times):
# weight3 = dt - 0.5*dt*(t3==0 or t3==len(times)-1)
# exp_iw3t3 = np.exp(1j*omega3*time3)
# for t2 in range(len(time2s)):
# spectrum[w3,t2,w1] += weight1*weight3*(
# exp_iw1t1*exp_iw3t3*Rsignal[1][t3,t2,t1]
# + exp_miw1t1*exp_iw3t3*Rsignal[0][t3,t2,t1] ).real
# #np.exp(1j*(omega1*time1+omega3*time3))*Rsignal[1][t3,t2,t1]
# #+np.exp(1j*(-omega1*time1+omega3*time3))*Rsignal[0][t3,t2,t1] ).real
print "done."
spectra = []
for t2 in range(len(time2s)):
spectra.append( spectrum[:,t2,:] )
return energy1s, energy3s, time2s, spectra, times, Rsignal
def absorption(self, e_min, e_max, de, rho_0, t_final, dt,
dipole_file='dipole_dipole.dat',
is_damped=True, lineshape_func = False):
utils.print_banner("CALCULATING LINEAR ABSORPTION SPECTRUM")
energies = np.arange(e_min, e_max, de)
omegas = energies/const.hbar
mu = self.dipole_site
t_damp=0.
if lineshape_func == True:
if self.dynamics.ham.nsite == 2:
omega_eg = self.dynamics.ham.omega_diff[1,0]
times = np.zeros(int(t_final/dt))
for n in range(len(times)):
times[n] = n*dt
# for t, time in enumerate(times):
# gt = self.dynamics.ham.sd[0].line_func(t*dt)
# print t*dt, gt.real
Cw = np.zeros(len(omegas))
expi = np.exp(1j*(np.outer(omegas,times)))
for t, time in enumerate(times):
weight = dt - 0.5*dt*(t==0 or t==len(times)-1)
gt = self.dynamics.ham.sd[0].line_func(t*dt)
# print 't=',t,'\ngt=',gt
Ct = np.exp(-1j*omega_eg*t*dt-gt)
if is_damped and t > t_damp:
Ct *= switch_to_zero(time,t_damp,t_final)
Cw += weight*(expi[:,t]*Ct).real
return energies, (mu[1,0]**2)*Cw
# if self.dynamics.ham.nsite == 3:
# nbath = self.dynamics.ham.nbath
# nsite = self.dynamics.ham.nsite
# omega_diff = self.dynamics.ham.omega_diff
# sys_eig = self.dynamics.ham.site2eig(self.dynamics.ham.sys)
# times = np.zeros(int(t_final/dt))
# sysbath_eig = []
# for n in range(nbath):
# sysbath_eig.append(self.dynamics.ham.site2eig(self.dynamics.ham.sysbath[n]))
# mu_eig = self.dynamics.ham.site2eig(mu)
#
# for n in range(len(times)):
# times[n] = n*dt
# # for t, time in enumerate(times):
# # gt = self.dynamics.ham.sd[0].line_func(t*dt)
# # print t*dt, gt.real
# Cw = np.zeros(len(omegas))
# expi = np.exp(1j*(np.outer(omegas,times)))
# print omega_diff
# for t, time in enumerate(times):
# weight = dt - 0.5*dt*(t==0 or t==len(times)-1)
# gt = self.dynamics.ham.sd[0].line_func(t*dt)
# pops1 = self.dynamics.ham.sd[0].sec_poprate(0.*omega_diff[0,2],t*dt)
# pops2 = self.dynamics.ham.sd[0].sec_poprate(0.*omega_diff[2,0],t*dt)
# Ct = np.exp(-1j*omega_diff[1,2]*t*dt-(sys_eig[2,2]**2)*gt-(sys_eig[0,2]**2)*pops1) + np.exp(-1j*omega_diff[0,1]*t*dt-(sys_eig[0,0]**2)*gt-50.*(sys_eig[2,0]**2)*pops2)
#
# if is_damped and t > t_damp:
# Ct *= switch_to_zero(time,t_damp,t_final)
# Cw += weight*(expi[:,t]*Ct).real
# return energies, (mu[1,0]**2)*Cw
else:
omega_diff = self.dynamics.ham.omega_diff
nbath = self.dynamics.ham.nbath
nsite = self.dynamics.ham.nsite
sys_eig = self.dynamics.ham.site2eig(self.dynamics.ham.sys)
sysbath_eig = []
for n in range(nbath):
sysbath_eig.append(self.dynamics.ham.site2eig(self.dynamics.ham.sysbath[n]))
mu_eig = self.dynamics.ham.site2eig(mu)
gs_index = np.where(np.diag(sys_eig) == 0.)[0][0]
markov_rate = []
for l in range(nbath):
markovrate_l = np.zeros((nsite,nsite))
for m in range(nsite):
for n in range(nsite):
markovrate_l[m,n] = self.dynamics.ham.sd[l].markov_poprate(omega_diff[n,m])
markovrate_l[n,n] = 0.0
markov_rate.append(markovrate_l)
times = np.zeros(int(t_final/dt))
for n in range(len(times)):
times[n] = n*dt
# for t, time in enumerate(times):
# gt = self.dynamics.ham.sd[0].sec_poprate(-1.,t*dt)
# print t*dt, gt.real
# print sys_eig
# print omega_diff
full_rate = np.zeros((nsite,nsite))
for n in range(nbath):
full_rate += (sysbath_eig[n]**2)*markov_rate[n]
# print full_rate
full_rate_sum = np.zeros(nsite)
for n in range(nsite):
full_rate_sum[n] = (np.sum(full_rate[n,:]))
# full_rate_sum = np.array([0.007806,0.,0.05768])
# # Coefficient for pure dephasing lineshape function on each site
gammas = np.zeros((nsite))
# print sysbath_eig
# print mu_eig
# print sys_eig
# print np.diag(sys_eig)
# print np.diag(sys_eig)[1]
for m in range(nbath):
for n in range(nsite):
gammas[n] += sysbath_eig[m][n,n]**2
t_damp = 0.
times = np.zeros(int(t_final/dt))
for n in range(len(times)):
times[n] = n*dt
expi = np.exp(1j*(np.outer(omegas,times)))
absw = np.zeros(len(omegas))
# Currently assumes all sites have identical J(w); not sure about individual J(w) after site to eig conversion
for n in range(nsite):
Cw = np.zeros(len(omegas))
for t, time in enumerate(times):
weight = dt - 0.5*dt*(t==0 or t==len(times)-1)
gt = self.dynamics.ham.sd[0].line_func(t*dt)
gt0 = self.dynamics.ham.sd[0].line_func(0.)
Ct = np.exp(-1j*omega_diff[n,gs_index]*t*dt-gammas[n]*(gt-gt0) - 0.5*full_rate_sum[n])
if is_damped and t > t_damp:
Ct *= switch_to_zero(time,t_damp,t_final)
Cw += weight*(expi[:,t]*Ct).real
absw += (mu_eig[n,gs_index]**2)*Cw
return energies, absw
# for l in range(nbath-1):
# for m in range(nsite-1):
# for n in range(nsite-1):
# self.dynamics.ham.sysbath_eig[0][2,1]**2)*self.dynamics.ham.sd[0].pop_rate(omega_diff[1,2]) + (self.dynamics.ham.sysbath_eig[1][2,1]**2)*self.dynamics.ham.sd[1].pop_rate(omega_diff[1,2])
# print self.dynamics.ham.sd[0].pop_rates(self.dynamics.ham.omega_diff)
# print "Analytical lineshape function is only implemented for the monomer case."
# expi = np.exp(1j*(np.outer(omegas,times)))
# weight = dt - 0.5*dt*(t==0 or t==len(times)-1)
# Ct = np.exp(-1j*omega_eg*t-self.dynamics.ham.sd[0].line_func(t*dt))
# Cw += weight*(expi[:,t]*Ct).real
else:
nbath = self.dynamics.ham.nbath
nsite = self.dynamics.ham.nsite
sysbath_eig = []
for n in range(nbath):
sysbath_eig.append(self.dynamics.ham.site2eig(self.dynamics.ham.sysbath[n]))
mu_rho_0 = np.dot(mu, rho_0)
times, mu_rho = self.dynamics.propagate(mu_rho_0, 0.0, t_final, dt)
Cw = np.zeros(len(omegas))
fdipole = open(dipole_file,'w')
t_damp = 0.
expi = np.exp(1j*np.outer(omegas,times))
for t, time in enumerate(times):
weight = dt - 0.5*dt*(t==0 or t==len(times)-1)
Ct = np.trace(np.dot(mu,mu_rho[t]))
if is_damped and t > t_damp:
Ct *= switch_to_zero(time,t_damp,t_final)
fdipole.write('%0.6f %0.6f %0.6f\n'%(
time, Ct.real, Ct.imag))
Cw += weight*(expi[:,t]*Ct).real
fdipole.close()
return energies, Cw
def __init__(self,
hamiltonian,
nmode=300,
ntraj=100,
dynamics=None,
omega_split=None,
use_PD=True):
"""Initialize the FrozenModes class.
Parameters
----------
hamiltonian : Hamiltonian
An instance of the pyrho Hamiltonian class
dynamics :
An instance of any pyrho dynamics class (e.g. Redfield)
nmode : int
The number of explicit classical modes to sample
ntraj : int
The number of trajectories over which to average
"""
utils.print_banner("PERFORMING FROZEN MODES DYNAMICS")
# .copy() is important to have an instance that is not updated by FM sampling
# FrozenModes.ham.sys must always be the original, dynamics.ham.sys will be
# updated in each realization
self.ham = hamiltonian.copy()
self.nmode = nmode
self.ntraj = ntraj
if dynamics is None:
# Pure frozen modes with unitary dynamics
self.dynamics = unitary.Unitary(hamiltonian)
else:
# "Hybrid" frozen modes with dissipative dynamics
self.dynamics = dynamics
if omega_split is None:
# Determine splitting frequency
omega_split = list()
if self.ham.nsite == 2:
omega_R = 2 * np.sqrt((ham[0, 0] - ham[1, 1])**2 / 4.0 +
ham[0, 1]**2) / const.hbar
else:
print "Automated splitting frequency for Nsys > 2 not implemented!"
raise SystemExit
for n in range(self.ham.nbath):
omega_split.append(omega_R / 4.)
else:
assert (len(omega_split) == self.ham.nbath)
for n in range(self.ham.nbath):
print "\n--- Splitting energy for bath %d = %0.2lf" % (
n, const.hbar * omega_split[n])
for n in range(self.ham.nbath):
Jslow, Jfast = partition_specdens(self.ham.sd[n].J,
omega_split[n], use_PD)
self.ham.sd[n].J, self.dynamics.ham.sd[n].J = Jslow, Jfast
