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measure_nucl_TK.py
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measure_nucl_TK.py
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#!/usr/bin/python
##########################################################################
# ELDEST #
# Investigating Electronic Decay Processes with Streaking #
##########################################################################
# Purpose: #
# - A program to simulate the time-resolved RICD spectroscopy #
# including classical nuclear dynamics. #
# #
##########################################################################
# written by: Elke Fasshauer May 2018 #
##########################################################################
import scipy
import scipy.integrate as integrate
from scipy.signal import argrelextrema
from scipy.special import erf
import numpy as np
import sciconv
import complex_integration as ci
import pulses
import in_out
import sys
import warnings
import potentials
# don't print warnings unless python -W ... is used
if not sys.warnoptions:
warnings.simplefilter("ignore")
infile = sys.argv[1]
print infile
#-------------------------------------------------------------------------
# open outputfile
outfile = open("eldest.out", mode='w')
pure_out = open('full.dat', mode='w')
movie_out = open('movie.dat', mode='w')
popfile = open("pop.dat", mode='w')
outfile.write("The results were obtained with time_save_measure_TK.py \n")
#-------------------------------------------------------------------------
# set some defaults
Xshape = 'convoluted'
#-------------------------------------------------------------------------
# read inputfile
(rdg_au, cdg_au,
Er_a_eV, Er_b_eV, tau_a_s, tau_b_s, E_fin_eV, tau_s, E_fin_eV_2, tau_s_2,
interact_eV,
Omega_eV, n_X, I_X, X_sinsq, X_gauss, Xshape,
omega_eV, n_L, I_L, Lshape, delta_t_s, shift_step_s, phi, q, FWHM_L,
tmax_s, timestep_s, E_step_eV,
E_min_eV, E_max_eV,
integ, integ_outer,
mass1, mass2, grad_delta, R_eq_AA,
V_RICD_in_a, V_RICD_in_b, V_RICD_in_c, V_RICD_in_d,
V_fin_RICD_a, V_fin_RICD_b,
V_ICD_in_a, V_ICD_in_b, V_ICD_in_c, V_ICD_in_d,
V_fin_ICD_a, V_fin_ICD_b) = in_out.read_input(infile, outfile)
#-------------------------------------------------------------------------
# Convert input parameters to atomic units
#-------------------------------------------------------------------------
Er_a_au = sciconv.ev_to_hartree(Er_a_eV)
Er_b_au = sciconv.ev_to_hartree(Er_b_eV)
Er_au = Er_a_au
E_fin_au = sciconv.ev_to_hartree(E_fin_eV)
E_fin_au_1 = sciconv.ev_to_hartree(E_fin_eV)
tau_au_1 = sciconv.second_to_atu(tau_s)
tau_au = tau_au_1
Gamma_au = 1. / tau_au
Gamma_eV = sciconv.hartree_to_ev(Gamma_au)
outfile.write('Gamma_eV = ' + str(Gamma_eV) + '\n')
# second final state
E_fin_au_2 = sciconv.ev_to_hartree(E_fin_eV_2)
tau_au_2 = sciconv.second_to_atu(tau_s_2)
Gamma_au_2 = 1. / tau_au_2
# laser parameters
Omega_au = sciconv.ev_to_hartree(Omega_eV)
if (X_sinsq):
TX_au = n_X * 2 * np.pi / Omega_au
elif(X_gauss):
sigma = np.pi * n_X / (Omega_au * np.sqrt(np.log(2)))
FWHM = 2 * np.sqrt( 2 * np.log(2)) * sigma
TX_au = 5 * sigma
print 'sigma = ', sciconv.atu_to_second(sigma)
print 'FWHM = ', sciconv.atu_to_second(FWHM)
outfile.write('sigma = ' + str(sciconv.atu_to_second(sigma)) + '\n')
outfile.write('FWHM = ' + str(sciconv.atu_to_second(FWHM)) + '\n')
print 'end of the first pulse = ', sciconv.atu_to_second(TX_au/2)
outfile.write('end of the first pulse = ' + str(sciconv.atu_to_second(TX_au)) + '\n')
I_X_au = sciconv.Wcm2_to_aiu(I_X)
print 'I_X = ', I_X
print 'I_X_au = ', I_X_au
E0X = np.sqrt(I_X_au)
A0X = E0X / Omega_au
print 'A0X = ', A0X
omega_au = sciconv.ev_to_hartree(omega_eV)
FWHM_L_au = sciconv.second_to_atu(FWHM_L)
sigma_L_au = FWHM_L_au / np.sqrt(8 * np.log(2))
a = 5./2 * sigma_L_au
print "FWHM_L = ", sciconv.atu_to_second(FWHM_L_au)
print "sigma_L = ", sciconv.atu_to_second(sigma_L_au)
TL_au = n_L * 2 * np.pi / omega_au
print 'start of IR pulse = ', delta_t_s - sciconv.atu_to_second(TL_au/2)
print 'end of IR pulse = ', delta_t_s + sciconv.atu_to_second(TL_au/2)
I_L_au = sciconv.Wcm2_to_aiu(I_L)
print 'I_L = ', I_L
print 'I_L_au = ', I_L_au
E0L = np.sqrt(I_L_au)
print 'E0L', E0L
A0L = E0L / omega_au
print 'A0L = ', A0L
delta_t_au = sciconv.second_to_atu(delta_t_s)
# parameters of the simulation
tmax_au = sciconv.second_to_atu(tmax_s)
timestep_au = sciconv.second_to_atu(timestep_s)
E_step_au = sciconv.ev_to_hartree(E_step_eV)
E_min_au = sciconv.ev_to_hartree(E_min_eV)
E_max_au = sciconv.ev_to_hartree(E_max_eV)
VEr_au = np.sqrt(Gamma_au/ (2*np.pi))
print 'VEr_au = ', VEr_au
WEr_au = np.sqrt(Gamma_au_2/ (2*np.pi))
VEr_au_1 = VEr_au
#test q=1
cdg_au_V = rdg_au / ( q * np.pi * VEr_au)
cdg_au_W = rdg_au / ( q * np.pi * WEr_au)
# parameters of the nuclear dynamics
red_mass_gmol = mass1 * mass2 / (mass1 + mass2)
red_mass = sciconv.gmol_to_me(red_mass_gmol)
#print red_mass_gmol
#print red_mass
R0 = sciconv.angstrom_to_bohr(R_eq_AA)
v0 = 0
T_K = 0
gammar6_a = Gamma_au * R0**6
gammar6_b = Gamma_au_2 * R0**6
#-------------------------------------------------------------------------
in_out.check_input(Er_au, E_fin_au, Gamma_au,
Omega_au, TX_au, n_X, A0X,
omega_au, TL_au, A0L, delta_t_au,
tmax_au, timestep_au, E_step_au)
#-------------------------------------------------------------------------
# physical defintions of functions
# functions for the shape of the XUV pulse
if (X_sinsq):
print 'use sinsq function'
f_t1 = lambda t1: 1./4 * ( np.exp(2j * np.pi * (t1 + TX_au/2) / TX_au)
+ 2
+ np.exp(-2j * np.pi * (t1 + TX_au/2) /TX_au) )
fp_t1 = lambda t1: np.pi/(2j*TX_au) * ( - np.exp(2j*np.pi* (t1 + TX_au/2) / TX_au)
+ np.exp(-2j*np.pi* (t1 + TX_au/2) / TX_au) )
elif (X_gauss):
print 'use gauss function'
f_t1 = lambda t1: ( 1./ np.sqrt(2*np.pi * sigma**2)
* np.exp(-t1**2 / (2*sigma**2)))
fp_t1 = lambda t1: ( -t1 / np.sqrt(2*np.pi) / sigma**3
* np.exp(-t1**2 / (2*sigma**2)))
else:
print 'no pulse shape selected'
if (Xshape == 'convoluted'):
FX_t1 = lambda t1: (
0
- (A0X
* np.cos(Omega_au * t1)
* fp_t1(t1)
)
+ (A0X
* Omega_au
* np.sin(Omega_au * (t1))
* f_t1(t1)
)
)
elif (Xshape == 'infinite'):
FX_t1 = lambda t1: + A0X * Omega_au * np.cos(Omega_au * t1)
#FX_t1 = lambda t1: - A0X * np.sin(Omega_au * t1)
# IR pulse
A_IR = lambda t3: A0L * np.sin(np.pi * (t3 - delta_t_au + TL_au/2) / TL_au)**2 \
* np.cos(omega_au * t3 + phi)
integ_IR = lambda t3: (p_au + A_IR(t3))**2
IR_during = lambda t2: np.exp(-1j * (E_kin_au + E_fin_au) * (t_au - t2))# \
IR_after = lambda t2: np.exp(-1j * E_kin_au * (t_au - t2)) #\
# population of the ICD initial state
Mr = lambda t1: N0 * (1
- np.exp(-1./2 * (erf((t1 - delta_t_au) / np.sqrt(2) / sigma_L_au)
-erf(-a/ np.sqrt(2) / sigma_L_au))) )
#-------------------------------------------------------------------------
# technical defintions of functions
#direct ionization
#fun_t_dir_1 = lambda t1: FX_t1(t1) * np.exp(1j * (E_fin_laser_au + TK_laser_au) * t1) \
# * np.exp(1j * E_kin_au * (t1-t_au)) \
# * np.exp(-1j * (TK_laser_au + E_fin_laser_au) * t_au)
# #* np.exp(-1j * (T_K + E_fin_au) * t_au)
fun_t_dir_1 = lambda t1: FX_t1(t1) * np.exp(1j * (E_fin_au + T_K) * t1) \
* np.exp(1j * E_kin_au * (t1-t_au)) \
* np.exp(-1j * (T_K + E_fin_au) * t_au)
#fun_TX2_dir_1 = lambda t1: FX_t1(t1) * np.exp(1j * E_fin_au * (t1-t_au)) \
# * np.exp(1j * E_kin_au * (t1-t_au))
fun_t_TX2_1 = lambda t1: FX_t1(t1) * np.exp(1j * (E_fin_au_TX2 + T_K_TX2) * t1) \
* np.exp(1j * E_kin_au * (t1-t_au)) \
* np.exp(-1j * (T_K_TX2 + E_fin_au_TX2) * t_au)
dress_I = lambda t1: integrate.quad(integ_IR,t1,t_au)[0]
dress = lambda t1: np.exp(-1j/2 * dress_I(t1))
dress_I_after = lambda t1: integrate.quad(integ_IR,t1,(delta_t_au + TL_au/2))[0]
dress_after = lambda t1: np.exp(-1j/2 * dress_I_after(t1))
fun_dress_after = lambda t1: FX_t1(t1) * np.exp(1j * E_fin_au * t1) \
* np.exp(1j * E_kin_au * ((delta_t_au + TL_au/2)-t_au)) \
* dress_after(t1)
fun_IR_dir = lambda t1: FX_t1(t1) * np.exp(1j * E_fin_au * t1) \
* dress(t1)
res_inner_fun = lambda t2: np.exp(-t2 * (np.pi * (VEr_au**2) + 1j*(Er_au))) \
* IR_during(t2)
if (integ == 'romberg'):
res_inner = lambda t1: integrate.romberg(res_inner_fun, t1, t_au)
elif (integ == 'quadrature'):
res_inner = lambda t1: integrate.quad(res_inner_fun, t1, t_au)[0]
elif (integ == 'analytic'):
# analytic inner integral
# res_inner = lambda t1: (
# np.exp(-t_au * 1j* (Er_au + T_K
# - 1j* np.pi * (VEr_au**2)))
# * np.exp(t1 * 1j* (Er_laser_au + TK_laser_au
# - 1j* np.pi * (VEr_au**2)))
# - np.exp(-1j* t_au * (E_kin_au + E_fin_au + T_K))
# * np.exp(1j* t1 * (E_kin_au + E_fin_laser_au + TK_laser_au))
# )
res_inner = lambda t1: (
np.exp(-t_au * 1j* (Er_au + T_K
- 1j* np.pi * (VEr_au**2)))
* np.exp(t1 * 1j* (Er_au + T_K
- 1j* np.pi * (VEr_au**2)))
- np.exp(-1j* t_au * (E_kin_au + E_fin_au + T_K))
* np.exp(1j* t1 * (E_kin_au + E_fin_au + T_K))
)
res_inner_sec = lambda t1: (
np.exp(-t_au * 1j* (Er_au
- 1j* np.pi * (VEr_au**2)))
* np.exp(t1 * 1j* (Er_laser_au
- 1j* np.pi * (VEr_laser_au**2)))
* np.exp(-delta_t_au * (1j*(E_kin_au + E_fin_au - Er_au)
- np.pi * (VEr_au**2)))
- np.exp(-1j* t_au * (E_kin_au + E_fin_au))
* np.exp(1j* t1 * (E_kin_au + E_fin_laser_au))
* np.exp(-delta_t_au * (1j*(E_kin_au + E_fin_laser_au - Er_laser_au)
- np.pi * (VEr_laser_au**2)))
)
#res_inner_sec = lambda t1: (1./(1j*(E_kin_au + E_fin_au - Er_au)
# - np.pi * (VEr_au**2))
# * (np.exp((t_au-delta_t_au) * (1j*(E_kin_au + E_fin_au - Er_au)
# - np.pi * (VEr_au**2)))
# - np.exp((t1-delta_t_au) * (1j*(E_kin_au + E_fin_au - Er_au)
# - np.pi * (VEr_au**2))))
# * np.exp(-1j*(t_au) * (E_kin_au + E_fin_au))
# )
res_outer_fun = lambda t1: FX_t1(t1) \
* 1./(1j*(E_kin_au + E_fin_au - Er_au)
- np.pi * (VEr_au**2)) \
* res_inner(t1)
second_outer_fun = lambda t1: A0X \
* 1./(1j*(E_kin_au + E_fin_au - Er_au)
- np.pi * (VEr_au**2)) \
* res_inner_sec(t1)
#second_outer_fun = lambda t1: A0X \
# * np.exp((t1) * (np.pi* (VEr_au**2) + 1j*Er_au)) \
# * res_inner_sec(t1) #\
# #* np.exp(-(t1 - delta_t_au)**2 / 2 / sigma_L_au**2)# \
# #/ np.sqrt(2*np.pi * sigma_L_au**2)
#-------------------------------------------------------------------------
# population change by tunnel ionization
Ip = sciconv.ev_to_hartree(1.5)
konst = 1./16
popfun = lambda t1: np.exp(-2* np.sqrt(2*Ip)**3 / 3 / A0L
* np.exp((t1-delta_t_au)**2 / 2 / sigma_L_au**2)) \
* konst
#-------------------------------------------------------------------------
#-------------------------------------------------------------------------
# initialization
t_au = -TX_au/2
# construct list of energy points
# test different energy areas
lower_E_min = sciconv.ev_to_hartree(0.45)
lower_E_max = sciconv.ev_to_hartree(0.75)
upper_E_min = sciconv.ev_to_hartree(0.0)
upper_E_max = E_max_au
Ekins1 = []
Ekins2 = []
E_kin_au = E_min_au
while (E_kin_au <= E_max_au):
if (E_kin_au >= lower_E_min and E_kin_au <= lower_E_max):
Ekins2.append(sciconv.hartree_to_ev(E_kin_au))
elif (E_kin_au >= upper_E_min and E_kin_au <= upper_E_max):
Ekins1.append(sciconv.hartree_to_ev(E_kin_au))
Ekins2.append(sciconv.hartree_to_ev(E_kin_au))
E_kin_au = E_kin_au + E_step_au
#-------------------------------------------------------------------------
# constants / prefactors
aV = VEr_au / np.sqrt(VEr_au**2 + WEr_au**2)
aW = WEr_au / np.sqrt(VEr_au**2 + WEr_au**2)
prefac_res1 = VEr_au * rdg_au
prefac_res2 = WEr_au
prefac_indir1 = -1j * np.pi * VEr_au**2 * cdg_au_V
prefac_indir2 = -1j * np.pi * WEr_au**2 * cdg_au_W
#prefac_indir = 0
prefac_dir1 = 1j * cdg_au_V
prefac_dir2 = 1j * cdg_au_W
N0 = 1. / 4 * rdg_au**2 * np.exp(-sigma**2 * (Omega_au - Er_a_au)**2) \
* np.exp(-Gamma_au * (delta_t_au - a))
#print "E_fin_au_1 = ", E_fin_au_1
#print "Er_a_au = ", Er_a_au
tmpfin = potentials.hyperbel(V_fin_RICD_a,V_fin_RICD_b,R0)
tmpEr = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R0)
E_fin_au_1 = tmpfin
Er_a_au = tmpEr
#print "E_fin_au_1 = ", E_fin_au_1
print "Er_a_au = ", sciconv.hartree_to_ev(Er_a_au)
#-------------------------------------------------------------------------
while ((t_au <= 0) and (t_au <= tmax_au)):
#-------------------------------------------------------------------------
outfile.write('during the first pulse \n')
print 'during the first pulse'
outlines = []
squares = np.array([])
E_kin_au = E_min_au
t_s = sciconv.atu_to_second(t_au)
print 't_s = ', sciconv.atu_to_second(t_au)
outfile.write('t_s = ' + str(sciconv.atu_to_second(t_au)) + '\n')
t_s = sciconv.atu_to_second(t_au)
movie_out.write('"' + format(t_s*1E15, '.3f') + ' fs' + '"' + '\n')
E_fin_laser_au = E_fin_au_1
Er_laser_au = Er_a_au
VEr_laser_au = VEr_au_1
TK_laser_au = 0
E_fin_au = E_fin_au_1
Er_au = Er_a_au
VEr_au = VEr_au_1
while (E_kin_au <= E_max_au):
p_au = np.sqrt(2*E_kin_au)
if (E_kin_au < upper_E_min):
square = 0.0
else:
# integral 1
if (integ_outer == "quadrature"):
E_fin_au = E_fin_au_1
Er_au = Er_a_au
VEr_au = VEr_au_1
I1 = ci.complex_quadrature(fun_t_dir_1, (-TX_au/2), t_au)
res_I = ci.complex_quadrature(res_outer_fun, (-TX_au/2), t_au)
dir_J1 = prefac_dir1 * I1[0]
res_J1 = prefac_res1 * res_I[0]
indir_J1 = prefac_indir1 * res_I[0]
elif (integ_outer == "romberg"):
E_fin_au = E_fin_au_1
Er_au = Er_a_au
VEr_au = VEr_au_1
I1 = ci.complex_romberg(fun_t_dir_1, (-TX_au/2), t_au)
res_I = ci.complex_romberg(res_outer_fun, (-TX_au/2), t_au)
dir_J1 = prefac_dir1 * I1
res_J1 = prefac_res1 * res_I
indir_J1 = prefac_indir1 * res_I
J = (0
+ dir_J1
+ res_J1
+ indir_J1
)
#outfile.write("Ekin, Jres = " + str(E_kin_au) + ' ' + str(res_J1)+'\n')
square = np.absolute(J)**2
squares = np.append(squares, square)
string = in_out.prep_output(square, E_kin_au, t_au)
outlines.append(string)
E_kin_au = E_kin_au + E_step_au
#print "vor dem Schreiben des Output"
in_out.doout_1f(pure_out, outlines)
in_out.doout_movie(movie_out, outlines)
# max_pos = argrelextrema(squares, np.greater)[0]
# #print "max_pos = ", max_pos
# #print "Ekins 2 = ", Ekins1[2], squares[2]
# if (len(max_pos > 0)):
# for i in range (0, len(max_pos)):
# #print "i = ", i
# print Ekins1[max_pos[i]], squares[max_pos[i]]
# outfile.write(str(Ekins1[max_pos[i]]) + ' ' + str(squares[max_pos[i]]) + '\n')
#print "vor dem naechsten Zeitschritt"
t_au = t_au + timestep_au
#print "nach dem ersten Teil"
#-------------------------------------------------------------------------
while ((t_au <= TX_au/2) and (t_au <= tmax_au)):
#-------------------------------------------------------------------------
outfile.write('during the first pulse \n')
print 'during the first pulse'
outlines = []
squares = np.array([])
E_kin_au = E_min_au
t_s = sciconv.atu_to_second(t_au)
print 't_s = ', sciconv.atu_to_second(t_au)
outfile.write('t_s = ' + str(sciconv.atu_to_second(t_au)) + '\n')
t_s = sciconv.atu_to_second(t_au)
movie_out.write('"' + format(t_s*1E15, '.3f') + ' fs' + '"' + '\n')
Vplus = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R0+grad_delta)
Vminus = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R0-grad_delta)
Vgrad = (Vplus - Vminus) / (2* grad_delta)
a = - Vgrad / red_mass
R = 0.5*a*timestep_au**2 + v0*timestep_au + R0
E_res_R = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R)
E_fin_R = potentials.hyperbel(V_fin_RICD_a,V_fin_RICD_b,R)
V_res_R = potentials.gammar6(gammar6_a,R)
R0 = R
v0 = a * timestep_au + v0
print "R0 = ", sciconv.bohr_to_angstrom(R0)
E_fin_laser_au = E_fin_au_1
Er_laser_au = Er_a_au
VEr_laser_au = VEr_au_1
TK_laser_au = 0
E_fin_au = E_fin_R
Er_au = E_res_R
T_K = Er_a_au - E_res_R
print "T_K [eV] = ", sciconv.hartree_to_ev(T_K)
if (E_res_R >= E_fin_R):
VEr_au = V_res_R
else:
VEr_au = 0
while (E_kin_au <= E_max_au):
p_au = np.sqrt(2*E_kin_au)
if (E_kin_au < upper_E_min):
square = 0.0
else:
# integral 1
if (integ_outer == "quadrature"):
I1 = ci.complex_quadrature(fun_t_dir_1, (-TX_au/2), t_au)
res_I = ci.complex_quadrature(res_outer_fun, (-TX_au/2), t_au)
dir_J1 = prefac_dir1 * I1[0]
res_J1 = prefac_res1 * res_I[0]
indir_J1 = prefac_indir1 * res_I[0]
elif (integ_outer == "romberg"):
I1 = ci.complex_romberg(fun_t_dir_1, (-TX_au/2), t_au)
res_I = ci.complex_romberg(res_outer_fun, (-TX_au/2), t_au)
dir_J1 = prefac_dir1 * I1
res_J1 = prefac_res1 * res_I
indir_J1 = prefac_indir1 * res_I
J = (0
+ dir_J1
+ res_J1
+ indir_J1
)
#outfile.write("Ekin, Jres = " + str(E_kin_au) + ' ' + str(res_J1)+'\n')
square = np.absolute(J)**2
squares = np.append(squares, square)
string = in_out.prep_output(square, E_kin_au, t_au)
outlines.append(string)
E_kin_au = E_kin_au + E_step_au
in_out.doout_1f(pure_out, outlines)
in_out.doout_movie(movie_out, outlines)
max_pos = argrelextrema(squares, np.greater)[0]
# if (len(max_pos > 0)):
# for i in range (0, len(max_pos)):
# print Ekins1[max_pos[i]], squares[max_pos[i]]
# outfile.write(str(Ekins1[max_pos[i]]) + ' ' + str(squares[max_pos[i]]) + '\n')
t_au = t_au + timestep_au
E_fin_au_TX2 = E_fin_R
T_K_TX2 = T_K
#-------------------------------------------------------------------------
while (t_au >= TX_au/2 and (t_au <= (delta_t_au - a)) and (t_au <= tmax_au)):
#-------------------------------------------------------------------------
outfile.write('between the pulses \n')
print 'between the pulses'
outlines = []
squares = np.array([])
E_kin_au = E_min_au
t_s = sciconv.atu_to_second(t_au)
movie_out.write('"' + format(t_s*1E15, '.3f') + ' fs' + '"' + '\n')
print 't_s = ', sciconv.atu_to_second(t_au)
outfile.write('t_s = ' + str(sciconv.atu_to_second(t_au)) + '\n')
Vplus = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R0+grad_delta)
Vminus = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R0-grad_delta)
Vgrad = (Vplus - Vminus) / (2* grad_delta)
a = - Vgrad / red_mass
R = 0.5*a*timestep_au**2 + v0*timestep_au + R0
E_res_R = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R)
E_fin_R = potentials.hyperbel(V_fin_RICD_a,V_fin_RICD_b,R)
V_res_R = potentials.gammar6(gammar6_a,R)
#print "E_res_R = ", E_res_R
#print "E_fin_R = ", E_fin_R
#print "V_res_R = ", V_res_R
R0 = R
v0 = a * timestep_au + v0
print "R0 = ", sciconv.bohr_to_angstrom(R0)
E_fin_laser_au = E_fin_au_1
Er_laser_au = Er_a_au
VEr_laser_au = VEr_au_1
TK_laser_au = 0
E_fin_au = E_fin_R
Er_au = E_res_R
VEr_au = V_res_R
T_K = Er_a_au - E_res_R
print "T_K [eV] = ", sciconv.hartree_to_ev(T_K)
if (E_res_R >= E_fin_R):
VEr_au = V_res_R
else:
VEr_au = 0
while (E_kin_au <= E_max_au):
p_au = np.sqrt(2*E_kin_au)
if (E_kin_au < upper_E_min):
square = 0.0
else:
# integral 1
if (integ_outer == "quadrature"):
I1 = ci.complex_quadrature(fun_t_TX2_1, (-TX_au/2), TX_au/2)
res_I = ci.complex_quadrature(res_outer_fun, (-TX_au/2), TX_au/2)
dir_J1 = prefac_dir1 * I1[0]
res_J1 = prefac_res1 * res_I[0]
indir_J1 = prefac_indir1 * res_I[0]
elif (integ_outer == "romberg"):
I1 = ci.complex_romberg(fun_t_TX2_1, (-TX_au/2), TX_au/2)
res_I = ci.complex_romberg(res_outer_fun, (-TX_au/2), TX_au/2)
dir_J1 = prefac_dir1 * I1
res_J1 = prefac_res1 * res_I
indir_J1 = prefac_indir1 * res_I
J = (0
+ dir_J1
+ res_J1
+ indir_J1
)
#outfile.write("Ekin, Jres = " + str(E_kin_au) + ' ' + str(res_J1)+'\n')
square = np.absolute(J)**2
squares = np.append(squares, square)
string = in_out.prep_output(square, E_kin_au, t_au)
outlines.append(string)
E_kin_au = E_kin_au + E_step_au
in_out.doout_1f(pure_out,outlines)
in_out.doout_movie(movie_out, outlines)
max_pos = argrelextrema(squares, np.greater)[0]
# if (len(max_pos > 0)):
# for i in range (0, len(max_pos)):
# print Ekins1[max_pos[i]], squares[max_pos[i]]
# outfile.write(str(Ekins1[max_pos[i]]) + ' ' + str(squares[max_pos[i]]) + '\n')
t_au = t_au + timestep_au
#-------------------------------------------------------------------------
while (t_au >= (delta_t_au - a) and (t_au <= (delta_t_au + a)) and (t_au <= tmax_au)):
#-------------------------------------------------------------------------
outfile.write('during the second pulse \n')
print 'during the second pulse'
outlines = []
squares = np.array([])
E_kin_au = E_min_au
t_s = sciconv.atu_to_second(t_au)
movie_out.write('"' + format(t_s*1E15, '.3f') + ' fs' + '"' + '\n')
print 't_s = ', sciconv.atu_to_second(t_au)
outfile.write('t_s = ' + str(sciconv.atu_to_second(t_au)) + '\n')
rdg_decay_au = np.sqrt(N0) \
* np.exp(-1./4 * 8 * (erf((t_au - delta_t_au) / np.sqrt(2) / sigma_L_au)
-erf(-a/ np.sqrt(2) / sigma_L_au) ) )
#rdg_decay_au = np.sqrt(N0) \
# * np.exp(-1./4 * (erf((t_au - delta_t_au))
# -erf(-a) ) )
#popint = ci.integrate.quad(popfun, delta_t_au - a, t_au)
#rdg_decay_au = np.sqrt(N0) * np.exp(-1./2 * popint[0])
print "sqrt N0 = ", np.sqrt(N0)
print "rdg_decay_au = ", rdg_decay_au
Mrt = np.sqrt(N0) - rdg_decay_au
prefac_res1 = VEr_au * rdg_decay_au
#prefac_dir1 = 1j * rdg_decay_au / q / np.pi / VEr_au
prefac_indir1 = -1j * VEr_au * rdg_decay_au / q
prefac_res2 = WEr_au * (np.sqrt(N0) - rdg_decay_au)
#prefac_res2 = WEr_au * np.sqrt(N0)
print "Mr(t) = ", (np.sqrt(N0) - rdg_decay_au)
popfile.write(str(sciconv.atu_to_second(t_au)) + ' ' + str(rdg_decay_au**2)
+ ' ' + str(Mrt**2) + '\n')
Vplus = potentials.expr6(V_ICD_in_a,V_ICD_in_b,V_ICD_in_c,V_ICD_in_d,R0+grad_delta)
Vminus = potentials.expr6(V_ICD_in_a,V_ICD_in_b,V_ICD_in_c,V_ICD_in_d,R0-grad_delta)
Vgrad = (Vplus - Vminus) / (2* grad_delta)
a = - Vgrad / red_mass
R = 0.5*a*timestep_au**2 + v0*timestep_au + R0
E_res_R = potentials.expr6(V_ICD_in_a,V_ICD_in_b,V_ICD_in_c,V_ICD_in_d,R)
E_fin_R = potentials.hyperbel(V_fin_ICD_a,V_fin_ICD_b,R)
V_res_R = potentials.gammar6(gammar6_b,R)
E_res_RICD = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R)
E_fin_RICD = potentials.hyperbel(V_fin_RICD_a,V_fin_RICD_b,R)
V_res_RICD = potentials.gammar6(gammar6_a,R)
R0 = R
v0 = a * timestep_au + v0
print "R0 = ", sciconv.bohr_to_angstrom(R0)
while (E_kin_au <= E_max_au):
p_au = np.sqrt(2*E_kin_au)
if (E_kin_au < lower_E_min):
square = 0.0
elif (E_kin_au > lower_E_max and E_kin_au < upper_E_min):
square = 0.0
elif (E_kin_au >= lower_E_min and E_kin_au <= lower_E_max):
# integral 1
if (integ_outer == "quadrature"):
E_fin_laser_au = E_fin_au_2
Er_laser_au = Er_b_au
VEr_laser_au = WEr_au
E_fin_au = E_fin_R
Er_au = E_res_R
VEr_au = V_res_R
res_I = ci.complex_quadrature(second_outer_fun, (- a),
(t_au-delta_t_au))
res_J2 = prefac_res2 * res_I[0]
elif (integ_outer == "romberg"):
E_fin_laser_au = E_fin_au_2
Er_laser_au = Er_b_au
VEr_laser_au = WEr_au
E_fin_au = E_fin_R
Er_au = E_res_R
VEr_au = V_res_R
res_I = ci.complex_romberg(second_outer_fun, (- a),
(t_au - delta_t_au))
res_J2 = prefac_res2 * res_I
square = np.absolute(res_J2)**2
squares = np.append(squares, square)
string = in_out.prep_output(square, E_kin_au, t_au)
outlines.append(string)
elif (E_kin_au >= upper_E_min and E_kin_au <= upper_E_max):
# integral 1
if (integ_outer == "quadrature"):
E_fin_laser_au = E_fin_au_1
Er_laser_au = Er_a_au
VEr_laser_au = VEr_au_1
E_fin_au = E_fin_RICD
Er_au = E_res_RICD
VEr_au = V_res_RICD
I1 = ci.complex_quadrature(fun_t_dir_1, (-TX_au/2), TX_au/2)
res_I = ci.complex_quadrature(res_outer_fun, (-TX_au/2), TX_au/2)
dir_J1 = prefac_dir1 * I1[0]
res_J1 = prefac_res1 * res_I[0]
indir_J1 = prefac_indir1 * res_I[0]
elif (integ_outer == "romberg"):
E_fin_laser_au = E_fin_au_1
Er_laser_au = Er_a_au
VEr_laser_au = VEr_au_1
E_fin_au = E_fin_RICD
Er_au = E_res_RICD
VEr_au = V_res_RICD
I1 = ci.complex_romberg(fun_t_dir_1, (-TX_au/2), TX_au/2)
res_I = ci.complex_romberg(res_outer_fun, (-TX_au/2), TX_au/2)
dir_J1 = prefac_dir1 * I1
res_J1 = prefac_res1 * res_I
indir_J1 = prefac_indir1 * res_I
J = (0
+ dir_J1
+ res_J1
+ indir_J1
)
square = np.absolute(J)**2
squares = np.append(squares, square)
string = in_out.prep_output(square, E_kin_au, t_au)
outlines.append(string)
E_kin_au = E_kin_au + E_step_au
in_out.doout_1f(pure_out,outlines)
in_out.doout_movie(movie_out, outlines)
max_pos = argrelextrema(squares, np.greater)[0]
if (len(max_pos > 0)):
for i in range (0, len(max_pos)):
print Ekins2[max_pos[i]], squares[max_pos[i]]
outfile.write(str(Ekins2[max_pos[i]]) + ' ' + str(squares[max_pos[i]]) + '\n')
t_au = t_au + timestep_au
popfile.close
prefac_res2 = WEr_au * np.sqrt(N0)
#-------------------------------------------------------------------------
while (t_au >= (delta_t_au + a) and (t_au <= tmax_au)):
#-------------------------------------------------------------------------
outfile.write('after the pulses \n')
print 'after the pulses'
outlines = []
squares = np.array([])
E_kin_au = E_min_au
t_s = sciconv.atu_to_second(t_au)
movie_out.write('"' + format(t_s*1E15, '.3f') + ' fs' + '"' + '\n')
print 't_s = ', sciconv.atu_to_second(t_au)
outfile.write('t_s = ' + str(sciconv.atu_to_second(t_au)) + '\n')
Vplus = potentials.expr6(V_ICD_in_a,V_ICD_in_b,V_ICD_in_c,V_ICD_in_d,R0+grad_delta)
Vminus = potentials.expr6(V_ICD_in_a,V_ICD_in_b,V_ICD_in_c,V_ICD_in_d,R0-grad_delta)
Vgrad = (Vplus - Vminus) / (2* grad_delta)
a = - Vgrad / red_mass
R = 0.5*a*timestep_au**2 + v0*timestep_au + R0
E_res_R = potentials.expr6(V_ICD_in_a,V_ICD_in_b,V_ICD_in_c,V_ICD_in_d,R)
E_fin_R = potentials.hyperbel(V_fin_ICD_a,V_fin_ICD_b,R)
V_res_R = potentials.gammar6(gammar6_b,R)
E_res_RICD = potentials.expr6(V_RICD_in_a,V_RICD_in_b,V_RICD_in_c,V_RICD_in_d,R)
E_fin_RICD = potentials.hyperbel(V_fin_RICD_a,V_fin_RICD_b,R)
V_res_RICD = potentials.gammar6(gammar6_a,R)
R0 = R
v0 = a * timestep_au + v0
print "R0 = ", sciconv.bohr_to_angstrom(R0)
while (E_kin_au <= E_max_au):
p_au = np.sqrt(2*E_kin_au)
if (E_kin_au < lower_E_min):
square = 0.0
elif (E_kin_au > lower_E_max and E_kin_au < upper_E_min):
square = 0.0
elif (E_kin_au >= lower_E_min and E_kin_au <= lower_E_max):
# integral 1
if (integ_outer == "quadrature"):
E_fin_laser_au = E_fin_au_2
Er_laser_au = Er_b_au
VEr_laser_au = WEr_au
E_fin_au = E_fin_R
Er_au = E_res_R
VEr_au = V_res_R
res_I = ci.complex_quadrature(second_outer_fun, (- a),
(+a))
res_J2 = prefac_res2 * res_I[0]
elif (integ_outer == "romberg"):
E_fin_laser_au = E_fin_au_2
Er_laser_au = Er_b_au
VEr_laser_au = WEr_au
E_fin_au = E_fin_R
Er_au = E_res_R
VEr_au = V_res_R
res_I = ci.complex_romberg(second_outer_fun, (- a),
(a))
res_J2 = prefac_res2 * res_I
square = np.absolute(res_J2)**2
squares = np.append(squares, square)
string = in_out.prep_output(square, E_kin_au, t_au)
outlines.append(string)
elif (E_kin_au >= upper_E_min and E_kin_au <= upper_E_max):
# integral 1
if (integ_outer == "quadrature"):
E_fin_laser_au = E_fin_au_1
Er_laser_au = Er_a_au
VEr_laser_au = VEr_au_1
E_fin_au = E_fin_RICD
Er_au = E_res_RICD
VEr_au = V_res_RICD
I1 = ci.complex_quadrature(fun_t_dir_1, (-TX_au/2), TX_au/2)
dir_J1 = prefac_dir1 * I1[0]
elif (integ_outer == "romberg"):
E_fin_laser_au = E_fin_au_1
Er_laser_au = Er_a_au
VEr_laser_au = VEr_au_1
E_fin_au = E_fin_RICD
Er_au = E_res_RICD
VEr_au = V_res_RICD
I1 = ci.complex_romberg(fun_t_dir_1, (-TX_au/2), TX_au/2)
dir_J1 = prefac_dir1 * I1
square = np.absolute(dir_J1)**2
squares = np.append(squares, square)
string = in_out.prep_output(square, E_kin_au, t_au)
outlines.append(string)
E_kin_au = E_kin_au + E_step_au
in_out.doout_1f(pure_out,outlines)
in_out.doout_movie(movie_out, outlines)
max_pos = argrelextrema(squares, np.greater)[0]
if (len(max_pos > 0)):
for i in range (0, len(max_pos)):
print Ekins2[max_pos[i]], squares[max_pos[i]]
outfile.write(str(Ekins2[max_pos[i]]) + ' ' + str(squares[max_pos[i]]) + '\n')
t_au = t_au + timestep_au
outfile.close
pure_out.close
movie_out.close