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 )
# Spectral densities - a list of length 'nbath'
lamda = 35.0
for [tau,T] in [[50.,77.], [50.,300.], [166.,300.]]:
#for [tau,T] in [[50.,77.]]:
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_ehrenfest = ehrenfest.Ehrenfest(my_ham, nmode=200, ntraj=500)
#for init in [1]:
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_ehrenfest.propagate(rho_0, 0.0, 1000.0, 0.5)
with open('pop_site_tau-%.0f_T-%.0f_init-%d.dat'
%(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_tau-%.0f_T-%.0f_init-%d.dat'
%(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')
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]])
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)
K = 0
for L in [1, 2, 4]:
lamda = 35.0
#tau = 50. # in fs
tau = 166. # in fs
omega_c = 1.0 / tau
for T in [300.]:
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_heom = heom.HEOM(my_ham, L=L, K=K)
for init in [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 = my_heom.propagate(rho_0, 0.0, 1000.0, 1.0)
with open(
'pop_site_T-%.0f_init-%d_tau-%.0f_L-%d_K-%d.dat' %
(T, init, tau, L, K), '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')
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 = 2
nbath = 1
V = 0.5
eps = 1 * V
kT = V / 0.5
# System Hamiltonian
ham_sys = np.array([[eps, V ],
[ V, -eps]])
# 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]])
eta = 6 * V
omega_c = 2 * V
lamda = eta * omega_c / (3.0 * 3.1416) * 2
# Spectral densities - a list of length 'nbath'
spec_densities = [['cubic-exp', lamda, omega_c]]*nbath
my_ham = ham.Hamiltonian(ham_sys, ham_sysbath, spec_densities, kT)
for K in [0]:
for L in [1,2]:
my_heom = heom.HEOM(my_ham, L=L, K=K, L_truncation='TL')
times, rhos_site = my_heom.propagate(rho_0, 0.0, 10.0/V, 0.01/V)
with open('pop_site_lam-%0.2f_L-%d_K-%d.dat'%(lamda,L,K), 'w') as f:
for (time, rho_site) in zip(times, rhos_site):
f.write('%0.8f %0.8f %0.8f\n'%(V*time, rho_site[0,0].real,
rho_site[1,1].real))
def main():
nbath = 2
kB = 0.69352 # in cm-1 / K
hbar = 5308.8 # in cm-1 * fs
# System Hamiltonian
# n = 0 is ground state
# One-exciton Hamiltonian
ham_sys_x = np.array([[-50., -100.], [-100., 50.]])
# One-exciton sys-bath coupling
nx = ham_sys_x.shape[0]
ham_sysbath_x = []
for b in range(nbath):
ham_sysbath_b = np.zeros((nx, nx))
for m in range(nx):
ham_sysbath_b[m, m] = (m == b)
ham_sysbath_x.append(ham_sysbath_b)
# One-exciton dipole moments
dipole_x = np.array([1., -0.2])
# Important: expand the Hilbert space (convert to biexciton space)
ham_sys, ham_sysbath, dipole = spec.convert_to_xx(ham_sys_x, ham_sysbath_x,
dipole_x)
nsite = ham_sys.shape[0]
lamda = 60.
omega_c = 1. / 100. # in 1/fs
kT = kB * 77.
spec_densities = [['ohmic-lorentz', lamda, omega_c]] * nbath
my_ham = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
# Numerical propagation parameters
t_final, dt = 500., 10.
# Waiting time parameters
T_init, T_final, dT = 0., 700., 100.
rho_g = np.zeros((nsite, nsite))
rho_g[0, 0] = 1.0
for K in [1]:
for L in [3]:
my_method = heom.HEOM(my_ham, L=L, K=K)
my_spec = spec.Spectroscopy(dipole, my_method)
omegas, intensities = my_spec.absorption(-400., 400., 2., rho_g,
t_final, dt)
with open(
'abs_HEOM_dt-%0.0f_tf-%0.0f_L-%d_K-%d.dat' %
(dt, t_final, L, K), 'w') as f:
for (omega, intensity) in zip(omegas, intensities):
f.write('%0.8f %0.8f\n' % (omega, intensity))
omega1s, omega3s, t2s, spectra = my_spec.two_dimensional(
-400., 400., 10., -400., 400., 10., T_init, T_final, dT, rho_g,
t_final, dt)
for t2, spectrum in zip(t2s, spectra):
with open(
'2d_t2-%0.1f_HEOM_dt-%0.0f_tf-%0.0f_L-%d_K-%d.dat' %
(t2, dt, t_final, L, K), 'w') as f:
for w1 in range(len(omega1s)):
for w3 in range(len(omega3s)):
f.write(
'%0.8f %0.8f %0.8f\n' %
(omega1s[w1], omega3s[w3], spectrum[w3, w1]))
f.write('\n')
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():
nsys = 3
nbath = 1
kT = 1.0
beta = 1.0 / kT
hbar = 1.0
K_list = [0]
L_list = [2]
single_harmonic = False
# Propagate until equilibrium
t_equil, dt = 2000., 0.1
# Propagate to retrieve TCF
T_init, T_final, dT = 0., 2000.0, 0.1
e_min, e_max, de = -2., +2., 0.01 # in unit of energy, cm-1
# Spectral densities - a list of length 'nbath'
sd_type = 'custom'
file_Jw = '../02_spectral_density/Data_fitted_Jw_parameters_updated_iteration03'
N_lorentz = 3
p_list, w_list, g_list = read_Jparameters(file_Jw, N_lorentz)
customPara = [p_list, w_list, g_list] # a 2d list
spec_densities = [['custom', customPara]] * nbath
File_Hs_DVR = '../01_DVR/Matrix_Hs'
File_rho_0 = '../01_DVR/Matrix_rho_0'
File_X_operator_DVR = '../01_DVR/Matrix_q_operator'
# System Hamiltonian, should be in unit of cm-1
ham_sys = read_2DMatrix(File_Hs_DVR, nsys)
# position operator
position = read_2DMatrix(File_X_operator_DVR, nsys)
# 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(position)
# Initial reduced density matrix of the system
rho_0 = read_2DMatrix(File_rho_0, nsys)
my_ham = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
for K in K_list:
for L in L_list:
my_method = heom.HEOM(my_ham, L=L, K=K)
my_equilTCF = equilTCF.EquilibriumTCF(position, my_method)
# First step: Equilibrate Dynamics
rho_hierarchy_equil, time1s, rhos_DVR = my_equilTCF.EquilibrateDynamics(
rho_0, t_equil, dt)
with open(
'pop_beta-%0.2f_dt-%0.2f_teqil-%0.0f_L-%d_K-%d_' %
(beta, dt, t_equil, L, K) + sd_type + '_500.dat', 'w') as f:
for (time, rho_DVR) in zip(time1s, rhos_DVR):
f.write('%0.8f ' % (time))
for i in range(nsys):
f.write('%0.8f ' % (rho_DVR[i, i].real))
f.write('\n')
# Second step: Evaluate TCF
if single_harmonic == True:
spec_densities = [[sd_type, 0.0, omega_c]] * nbath
my_ham = ham.Hamiltonian(ham_sys,
ham_sysbath,
spec_densities,
kT,
hbar=hbar)
my_method = heom.HEOM(my_ham, L=L, K=K)
my_equilTCF = equilTCF.EquilibriumTCF(position, my_method)
time2s, Ct, Ct_damp, omegas, Cw, Cw_damp, Dw = my_equilTCF.EvaluateTCF(
rho_hierarchy_equil, T_init, T_final, dT, e_min, e_max, de)
with open(
'Ct_beta-%0.2f_teqil-%0.0f_dT-%0.3f_Tfinal-%0.0f_L-%d_K-%d.dat'
% (beta, t_equil, dT, T_final, L, K), 'w') as f1:
for (t, intensity) in zip(time2s, Ct):
f1.write('%0.8f %0.8f %0.8f\n' %
(t, intensity.real, intensity.imag))
with open(
'CtDamp_beta-%0.2f_teqil-%0.0f_dT-%0.3f_Tfinal-%0.0f_L-%d_K-%d.dat'
% (beta, t_equil, dT, T_final, L, K), 'w') as f2:
for (t, intensity) in zip(time2s, Ct_damp):
f2.write('%0.8f %0.8f %0.8f\n' %
(t, intensity.real, intensity.imag))
with open(
'Cw_beta-%0.2f_teqil-%0.0f_dT-%0.3f_Tfinal-%0.0f_L-%d_K-%d.dat'
% (beta, t_equil, dT, T_final, L, K), 'w') as f3:
for (omega, intensity) in zip(omegas, Cw):
f3.write('%0.8f %0.8f\n' % (omega, intensity))
with open(
'CwDamp_beta-%0.2f_teqil-%0.0f_dT-%0.3f_Tfinal-%0.0f_L-%d_K-%d.dat'
% (beta, t_equil, dT, T_final, L, K), 'w') as f3:
for (omega, intensity) in zip(omegas, Cw_damp):
f3.write('%0.8f %0.8f\n' % (omega, intensity))
with open(
'Dw_beta-%0.2f_teqil-%0.0f_dT-%0.3f_Tfinal-%0.0f_L-%d_K-%d.dat'
% (beta, t_equil, dT, T_final, L, K), 'w') as f5:
for (omega, intensity) in zip(omegas, Dw):
f5.write('%0.8f %0.8f %0.8f\n' %
(omega, intensity.real, intensity.imag))
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))
