def analytic_R0(Gamma_L, Gamma_R):
return np.array([[Gamma_L**2 + Gamma_L*Gamma_R, -Gamma_R**2 - Gamma_L*Gamma_R],
[-Gamma_L**2 - Gamma_L*Gamma_R, Gamma_R**2 + Gamma_L*Gamma_R]]) / (Gamma_L + Gamma_R)**3
def zero_freq_noise(liouvillian, jump_liouvillian, sys_dim, stationary_state, dv_pops, Gamma_L, Gamma_R):
J_1 = cs.differentiate_jump_matrix(jump_liouvillian)
Q = np.eye(sys_dim**2) - np.outer(stationary_state, dv_pops)
R0 = np.dot(Q, np.dot(la.pinv2(-liouvillian), Q)) #analytic_R0(Gamma_L, Gamma_R) #
noise = - cs.trace_density_vector(np.dot(cs.differentiate_jump_matrix(J_1), stationary_state), dv_pops) \
- 2. * cs.trace_density_vector(np.dot(np.dot(np.dot(J_1, R0), J_1), stationary_state), dv_pops)
return noise
def analytic_F2(Gamma_L, Gamma_R):
return (Gamma_L**2 + Gamma_R**2) / (Gamma_L + Gamma_R)**2
Gamma_L = 1.
Gamma_R = 2.
L = np.array([[-Gamma_L,Gamma_R],
[Gamma_L,-Gamma_R]])
LJ = np.array([[0,Gamma_R],
[0,0]])
dv_pops = np.array([1,1])
ss = utils.stationary_state(L, dv_pops)
print L
print analytic_R0(Gamma_L, Gamma_R)
print ss
print zero_freq_noise(L, LJ, np.sqrt(2), ss, dv_pops, Gamma_L, Gamma_R) / (Gamma_R*ss[-1])
print analytic_F2(Gamma_L, Gamma_R)
print '[Executing script...]'
# set up data
model = DimerVibModel() # model should be a subclass of DataModel
# first compare analytic and numerical zero-freq noise calculations
num_data_pts = 180
energy_gap_range = np.linspace(-2,3,num_data_pts)
F2 = np.zeros(num_data_pts)
#current = np.zeros(num_data_pts)
for i,E in enumerate(energy_gap_range):
print 'calculating for energy gap ' + str(E)
model.energy_gap = E
L = model.liouvillian
L_jump = model.jump_liouvillian
dv_pops = np.eye(3*model.vib_basis_size).flatten()
#dv_pops = np.delete(dv_pops, model.element_indices_to_remove, 0)
dv = utils.stationary_state(L(0), dv_pops)
#current[i] = cs.mean(L(0), L_jump(0), dv, dv_pops)
F2[i] = cs.zero_freq_noise(L, dv_pops) / cs.mean(L(0), L_jump(0), dv, dv_pops)
np.savez('../../data/dimer_vib_energy_gap_zero_freq_F2_data.npz', energy_gap_range=energy_gap_range, F2=F2)
plt.plot(energy_gap_range, F2)
plt.show()
#easygui.msgbox('Script execution complete!', title='PyDev Alert')
print '[Script execution complete]'
import matplotlib.pyplot as plt
from vibration_counting_statistics.dimer_vib_model import DimerVibModel
freq_range = np.linspace(0, 2.5, 100)
model = DimerVibModel()
model.J = 0.2
F2 = np.zeros((3, freq_range.size))
model.mode_coupling = 0
L = model.liouvillian
L_dim = L().shape[0]
L_jump = model.jump_liouvillian
dm_pops = np.eye(np.sqrt(L_dim)).flatten()
ss = utils.stationary_state(L(), populations=dm_pops)
F2[0] = cs.second_order_fano_factor(L, L_jump, ss, freq_range, dm_pops)
model.mode_coupling = 0.3
mode_freq_vals = np.array([1., 2.])
for i,freq in enumerate(mode_freq_vals):
model.omega = freq
L = model.liouvillian
L_dim = L().shape[0]
L_jump = model.jump_liouvillian
dm_pops = np.eye(np.sqrt(L_dim)).flatten()
ss = utils.stationary_state(L(), populations=dm_pops)
F2[i+1] = cs.second_order_fano_factor(L, L_jump, ss, freq_range, dm_pops)
np.savez('../../data/dimer_vib_finite_freq_F2_data.npz', freq_range=freq_range, F2=F2, mode_freq_vals=mode_freq_vals)
for i,v in enumerate(mode_dampings):
print 'Calculations for v = ' + str(v)
#model.mode_coupling = v
#model.N = v
model.vib_damping_rate = v
temp_current = np.zeros(num_data_pts)
#temp_current_cs = np.zeros(num_data_pts)
for j,e in enumerate(energy_gap_range):
model.energy_gap = e
L = model.liouvillian()
dm_pops = np.eye(3*model.vib_basis_size).flatten()
ss_vec = utils.stationary_state(L, dm_pops)
ss_mat = ss_vec.copy()
ss_mat.shape = np.sqrt(ss_mat.shape[0]), np.sqrt(ss_mat.shape[0])
ss_el = utils.partial_trace(ss_mat, utils.orthog_basis_set(model.vib_basis_size))
temp_current[j] = model.Gamma_R * ss_el[2,2]
#temp_current_cs[j] = cs.mean(L, model.jump_liouvillian(), ss_vec, dm_pops)
current[i] = temp_current
plt.plot(energy_gap_range, current[i], label=v)
#np.savez('../../data/dimer_vib_energy_gap_current_mode_coupling_data.npz', energy_gap_range=energy_gap_range, current=current, mode_couplings=mode_couplings)
#np.savez('../../data/dimer_vib_energy_gap_current_thermal_occupation_data.npz', energy_gap_range=energy_gap_range, current=current, thermal_occupations=thermal_occupations)
np.savez('../../data/dimer_vib_energy_gap_current_mode_damping_data.npz', energy_gap_range=energy_gap_range, current=current, mode_dampings=mode_dampings)
#plt.plot(energy_gap_range, current_cs)
plt.legend()