Spin-Boson Model (Debye Spectral Density)

This section demonstrates the simulation of the spin-boson model.

The model parameters must be specified in the following order: model \(\text{ spinboson} \quad \epsilon \quad \Delta \quad \text{enu}\)

The bath parameters are specified as: spectra \(\textit{ *bath-type*} \quad E_r \quad \omega_c \quad T\)

Note

  • All spin-boson parameters are given in energy unit of \(\text{cm}^{-1}\) and scale by the factor enu.

  • If enu = 1, then all parameters are expressed in atomic units.

Prepare param.in

Prepare input file param.in for spin-boson model with appropriate model parameters.

#SHARP Pack INPUT PARAMETERS
model      spinboson 0.0 1.0 104.25
spectra    debye 1.0 1.0 2.0
nParticle  100
nbeads     4
approx     CA
nmode      matrix
nsteps     20670
ntraj      1000
ncore      1
tstep      1.0
rsamp      gaussian
rmode      norm
rmap       no
vsamp      gaussian
VReverse   always
Vrescale   BL
rundtail   Yes
iprint     10
finish

Run Simulation

Run the simulation using one of the following methods:

# direct execution
$ ./sharp.x

# for running on a local machine
$ sh job-script-local.sh

#for submitting jobs on an HPC cluster (Slurm)
$ sh job-script-hpc.sh

Plot Result

Use gnuplot script plot-pop.gnu to plot population dynamics.

#!/usr/bin/gnuplot
set terminal pdf size 4in,3in enhanced color font 'Helvetica,16'
set border lw 2.5
set tics scale 1.2
set multiplot layout 1,1
set xlabel 'Time (a.u.)'
set ylabel 'P_1'
set yr[0:1]
set xr[0:0.5]

heom = 'heom-result/exact-qutip-lambda1-d1-w1-t300.dat'
set output 'fig-spinboson-pop.pdf'
set key  samplen 1.0 spacing 1.3 font "Helvetica, 14"
plot heom every 25 u 1:2 w p lc 0 pt 7 ps 0.6 t'Exact',\
     'pop_diabat3.out' u (column(1)/41340):2 w l ls 6 lw 5 t'RPSH'
Population dynamics of spin-boson model

Fig. 5 Population dynamics of spin-boson model at temperature 300 K and reorganization energy, \(E_r = 0.02\).