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8 Quantum Ratchets
8.2.2 Program 8.1b, Complete Langevin Equation, Matlab
Code
clear;
%Dimensionless Complete Langevin Equation with aceleration,
N=230000; NR=1; kL=1.; C1=0.; Fext=0.; FDN=0.;
dhp=1.; dGamma=0.1; x00=1.e-6; Uo= 1; dkBT=1.;
M=1.; dt=1.e-4; E11=1.6; E22=1.98; w=1.; r=0.5; theta=r*2*pi;
%=========================================================
% QUANTUM PARAMETERS and limits for the noise
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% Here the unit of energy is Uo.
Dbeta=Uo./dkBT;
%=========================================================
%Parameters from S. Denisov et al. Europhys. Lett. 85, 40003, (2009).
%=========================================================
qrt(Uo/M) ts=(1/kL)*sqrt(M/Uo);
Gamma=dGamma/ts;
GAMMA=M*Gamma;
kBT=Uo*dkBT;
hp=(dhp/kL)*sqrt(M*Uo);
tc=hp/(2*pi*kBT);%Thermal correlation time
nu=2*pi*kBT/hp; %(for T = 1pK, nu=0.0417/s FIRST MATSUBARA FREQUENCY.
y=1+(tc*Gamma/pi);
lambda=(hp/(pi*GAMMA))*(-psi(0,1) + psi(0,y));
Dlambda=lambda*kL 2
%Dlambda=0.; To use when you want simulate classical regime.
%=========================================================
%CLASSICAL RANGE gamma « nu,
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%QUANTUM RANGE gamma » nu
%=========================================================
F=(1:N)*0;
F=F’;
F1=(1:N)*0;
F1=F1’;
x=zeros(N,NR);
v=zeros(N,NR);
xij=x00;
v(1,1)=0.;
%=========================================================
% DICHOTOMOUS NOISE (iN CASE YOU WANT TO USE)
%=========================================================