def main():
nsite = 2
nbath = 2
kB = 0.69352 # in cm-1 / K
kT = kB * 300.0
hbar = 5308.8 # in cm-1 * fs
# System Hamiltonian
ham_sys = np.array([[100.0, 100.0], [100.0, 0.0]])
# System part of the the system-bath interaction
# - a list of length 'nbath'
# - currently assumes that each term has uncorrelated bath operators
ham_sysbath = []
ham_sysbath.append(np.array([[1.0, 0.0], [0.0, 0.0]]))
ham_sysbath.append(np.array([[0.0, 0.0], [0.0, 1.0]]))
# Initial reduced density matrix of the system
rho_0 = np.array([[1.0, 0.0], [0.0, 0.0]])
for lamda in [100. / 50, 100. / 5, 100., 500.]:
for tau_c in [100., 500.]:
omega_c = 1.0 / tau_c # in 1/fs
# Spectral densities - a list of length 'nbath'
spec_densities = [['ohmic-lorentz', lamda, omega_c]] * nbath
my_ham = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
for method in ['Redfield', 'TCL2']:
my_redfield = redfield.Redfield(my_ham, method=method)
times, rhos_site, rhos_eig = my_redfield.propagate(
rho_0, 0.0, 1000.0, 1.0)
with open(
'pop_site_%s_tau-%0.1f_lam-%0.2f.dat' %
(method, tau_c, lamda), 'w') as f:
for (time, rho_site,
rho_eig) in zip(times, rhos_site, rhos_eig):
f.write(
'%0.8f %0.8f %0.8f\n' %
(time, rho_site[0, 0].real, rho_site[1, 1].real))
def main():
nsite = 2
nbath = 1
# System Hamiltonian
ham_sys = np.array([[1.0, 1.0], [1.0, -1.0]])
# System part of the the system-bath interaction
# - a list of length 'nbath'
# - currently assumes that each term has uncorrelated bath operators
ham_sysbath = []
ham_sysbath.append(np.array([[1.0, 0.0], [0.0, -1.0]]))
# Initial reduced density matrix of the system
rho_0 = np.array([[1.0, 0.0], [0.0, 0.0]])
for alpha in [0.1, 0.2, 0.4]:
# Spectral densities - a list of length 'nbath'
omega_c = 7.5
lamda = alpha * omega_c / 2.0
spec_densities = [['ohmic-exp', lamda, omega_c]] * nbath
kT = 0.2
my_ham = ham.Hamiltonian(ham_sys, ham_sysbath, spec_densities, kT)
for method in ['Redfield', 'TCL2', 'TC2']:
if method == 'Redfield':
is_secular = True
else:
is_secular = False
my_redfield = redfield.Redfield(my_ham,
method=method,
is_secular=is_secular)
times, rhos_site, rhos_eig = my_redfield.propagate(
rho_0, 0.0, 14.0, 0.05)
with open('pop_site_%s_alpha-%0.2f.dat' % (method, alpha),
'w') as f:
for (time, rho_site, rho_eig) in zip(times, rhos_site,
rhos_eig):
f.write('%0.8f %0.8f %0.8f\n' %
(time, rho_site[0, 0].real, rho_site[1, 1].real))
def main():
nsite = 1 + 2
nbath = 2
eps = 0.
# System Hamiltonian
# n = 0 is ground state
ham_sys = np.array([[0., 0., 0.], [0., eps, -1.], [0., -1., eps]])
# System part of the the system-bath interaction
ham_sysbath = []
for n in range(1, nsite):
ham_sysbath_n = np.zeros((nsite, nsite))
ham_sysbath_n[n, n] = 1.0
ham_sysbath.append(ham_sysbath_n)
rho_g = np.zeros((nsite, nsite))
rho_g[0, 0] = 1.0
# Dipole operator connecting the ground state to the excited states
dipole = np.array([[0., 1., 1.], [1., 0., 0.], [1., 0., 0.]])
lamda = 0.5
omega_c = 1.0
beta = 3.0
kT = 1. / beta
spec_densities = [['ohmic-lorentz', lamda, omega_c]] * nbath
my_ham = ham.Hamiltonian(ham_sys, ham_sysbath, spec_densities, kT)
my_redfield = redfield.Redfield(my_ham, method='Redfield', is_secular=True)
dt = 0.05
t_final = 50.0
my_spec = spec.Spectroscopy(dipole, my_redfield)
omegas, intensities = my_spec.absorption(-4. + eps, 4. + eps, 0.02, rho_g,
0., t_final, dt)
with open('abs_omegac-%0.1f_beta-%0.1f.dat' % (omega_c, beta), 'w') as f:
for (omega, intensity) in zip(omegas, intensities):
f.write('%0.8f %0.8f\n' % (omega - eps, intensity))
def main():
nsite = 3
nbath = 2
eps = 0.
ham_sys = np.array([[0., 0., 0.], [0., eps, -1.], [0., -1., eps]])
ham_sysbath = []
for n in range(1, nsite):
ham_sysbath_n = np.zeros((nsite, nsite))
ham_sysbath_n[n, n] = 1.0
ham_sysbath.append(ham_sysbath_n)
rho_g = np.zeros((nsite, nsite))
rho_g[0, 0] = 1.0
dipole = np.array([[0., 1., 1.], [1., 0., 0.], [1., 0., 0.]])
lamda = 1. / 2
for omega_c in [0.1, 0.3, 1.0]:
for beta in [1.0, 3.0]:
kT = 1. / beta
spec_densities = [['ohmic-lorentz', lamda, omega_c]] * nbath
my_ham = ham.Hamiltonian(ham_sys, ham_sysbath, spec_densities, kT)
for method in ['HEOM', 'TL', 'TNL']:
emin, emax, de = -4 + eps, 4 + eps, 0.02
t_final = 50.0
dt = 0.05
if method == 'HEOM':
# These are a bit underconverged; they are TNL(N=8) in the paper.
for L in [4]:
for K in [1]:
my_method = heom.HEOM(my_ham, L=L, K=K)
my_spec = spec.Spectroscopy(dipole, my_method)
omegas, intensities = my_spec.absorption(
emin, emax, de, rho_g, t_final, dt)
with open(
'abs_omegac-%0.1f_beta-%0.1f_HEOM_L-%d_K-%d.dat'
% (omega_c, beta, L, K), 'w') as f:
for (omega,
intensity) in zip(omegas, intensities):
f.write('%0.8f %0.8f\n' %
(omega - eps, intensity))
else:
if method == 'TL':
my_method = redfield.Redfield(my_ham, method='TCL2')
else:
my_method = redfield.Redfield(my_ham, method='TC2')
t_final = 100.0
my_spec = spec.Spectroscopy(dipole, my_method)
omegas, intensities = my_spec.absorption(
emin, emax, de, rho_g, t_final, dt)
with open(
'abs_omegac-%0.1f_beta-%0.1f_%s.dat' %
(omega_c, beta, method), 'w') as f:
for (omega, intensity) in zip(omegas, intensities):
f.write('%0.8f %0.8f\n' % (omega - eps, intensity))
def main():
nbath = 2
kB = 0.69352 # in cm-1 / K
kT = kB * 300.0
hbar = 5308.8 # in cm-1 * fs
# System Hamiltonian
ham_sys = np.array([[100.0, 100.0], [100.0, 0.0]])
# System part of the the system-bath interaction
# - a list of length 'nbath'
# - currently assumes that each term has uncorrelated bath operators
ham_sysbath = []
ham_sysbath.append(np.array([[1.0, 0.0], [0.0, 0.0]]))
ham_sysbath.append(np.array([[0.0, 0.0], [0.0, 1.0]]))
# Initial reduced density matrix of the system
rho_0 = np.array([[1.0, 0.0], [0.0, 0.0]])
for lamda in [100. / 50, 100. / 5, 100., 500.]:
for tau_c in [100., 500.]:
omega_c = 1.0 / tau_c # in 1/fs
# Spectral densities - a list of length 'nbath'
spec_densities = [['ohmic-lorentz', lamda, omega_c]] * nbath
#TODO(TCB): Make this cleaner. Write a Hamiltonian.copy() method?
my_ham = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
my_ham_slow = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
my_ham_fast = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
ntraj = int(1e3)
my_frozen = frozen.FrozenModes(my_ham_slow, nmode=300, ntraj=ntraj)
times, rhos_site, rhos_eig = my_frozen.propagate(
rho_0, 0.0, 1000.0, 1.0)
my_redfield = redfield.Redfield(my_ham_fast, method='Redfield')
my_hybrid = hybrid.Hybrid(my_ham,
my_frozen,
my_redfield,
omega_split=None)
times, rhos_site, rhos_eig = my_hybrid.propagate(
rho_0, 0.0, 1000.0, 1.0)
with open(
'pop_site_tau-%0.1f_lam-%0.2f_ntraj-%d.dat' %
(tau_c, lamda, ntraj), 'w') as f:
for (time, rho_site, rho_eig) in zip(times, rhos_site,
rhos_eig):
f.write('%0.8f %0.8f %0.8f\n' %
(time, rho_site[0, 0].real, rho_site[1, 1].real))
def main():
nsite = 7
nbath = 7
kB = 0.69352 # in cm-1 / K
hbar = 5308.8 # in cm-1 * fs
# System Hamiltonian in cm-1
ham_sys = np.array([[12410, -87.7, 5.5, -5.9, 6.7, -13.7, -9.9],
[-87.7, 12530, 30.8, 8.2, 0.7, 11.8, 4.3],
[5.5, 30.8, 12210, -53.5, -2.2, -9.6, 6.0],
[-5.9, 8.2, -53.5, 12320, -70.7, -17.0, -63.3],
[6.7, 0.7, -2.2, -70.7, 12480, 81.1, -1.3],
[-13.7, 11.8, -9.6, -17.0, 81.1, 12630, 39.7],
[-9.9, 4.3, 6.0, -63.3, -1.3, 39.7, 12440]])
# System part of the the system-bath interaction
# - a list of length 'nbath'
# - currently assumes that each term has uncorrelated bath operators
ham_sysbath = []
for n in range(nbath):
ham_sysbath_n = np.zeros((nsite, nsite))
ham_sysbath_n[n, n] = 1.0
ham_sysbath.append(ham_sysbath_n)
for method in ['Redfield', 'TCL2', 'TC2']:
# Spectral densities - a list of length 'nbath'
lamda = 35.0
for [tau, T] in [[50., 77.], [50., 300.], [166., 300.]]:
omega_c = 1.0 / tau # in 1/fs
kT = kB * T
spec_densities = [['ohmic-lorentz', lamda, omega_c]] * nbath
my_ham = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
my_redfield = redfield.Redfield(my_ham, method=method)
for init in [1, 6]:
# Initial reduced density matrix of the system
rho_0 = np.zeros((nsite, nsite))
rho_0[init - 1, init - 1] = 1.0
times, rhos_site, rhos_eig = my_redfield.propagate(
rho_0, 0.0, 1000.0, 1.0, markov_time=3 * tau)
with open(
'pop_site_%s_tau-%.0f_T-%.0f_init-%d.dat' %
(method, tau, T, init), 'w') as f:
for (time, rho_site) in zip(times, rhos_site):
f.write('%0.8f ' % (time))
for i in range(nsite):
f.write('%0.8f ' % (rho_site[i, i].real))
f.write('\n')
with open(
'pop_eig_%s_tau-%.0f_T-%.0f_init-%d.dat' %
(method, tau, T, init), 'w') as f:
for (time, rho_eig) in zip(times, rhos_eig):
f.write('%0.8f ' % (time))
for i in range(nsite):
f.write('%0.8f ' % (rho_eig[i, i].real))
f.write('\n')