146
8 Quantum Ratchets
t2=0.01425; D2=A2*t2;
t3=0.3896; D3=A3*t3;
DDeff=zeros(N-1,NR);
eps=zeros(N-1,NR);
h=zeros(N-1,NR);
eps1=zeros(N-1,NR);
h1=zeros(N-1,NR);
eps2=zeros(N-1,NR);
h2=zeros(N-1,NR);
eps3=zeros(N-1,NR);
h3=zeros(N-1,NR);
a1 = abs(randn(1));
b1 = abs(randn(1));
a2 = abs(randn(1));
b2 = abs(randn(1));
a3 = abs(randn(1));
b3 = abs(randn(1));
E1 = exp(-(dt/(t1*tR)));
E2 = exp(-(dt/(t2*tR)));
E3 = exp(-(dt/(t3*tR)));
eps1(1,1) = sqrt((-2.*(DDeff(1,1)*D1)/(t1*tR))*(1-E1 2 )*log(a1))*cos(2*pi*b1);
eps2(1,1) = sqrt((-2.*(DDeff(1,1)*D2)/(t2*tR))*(1-E2 2 )*log(a2))*cos(2*pi*b2);
eps3(1,1) = sqrt((-2.*(DDeff(1,1)*D3)/(t3*tR))*(1-E3 2 )*log(a3))*cos(2*pi*b3);
eps(1,1)=eps1(1,1)+eps2(1,1)+eps3(1,1);
for j=1:NR
xij=x00;
v(1,1)=0.;
disp(j)
for i=2:N-1
xij=x(i,j);
%========================================================
Dd1U(i,j)=-sin(kL*xij) + C1* 0.5*sin(2.*xij);
Dd2U(i,j)=-cos(kL*xij) + C1*cos(2.*kL*xij);
Dd3U(i,j)=sin(kL*xij) - C1*2.*sin(2.*kL*xij);
DDeff(i,j)=1./(1-Dlambda*Dbeta*Dd2U(i,j));
%========================================================
% QUANTUM LANGEVIN EQUATION
%========================================================
F(i)= E11*cos(w*(i-1)*dt)+E22*cos(2*w*(i-1)*dt + theta);
F1(i)= -(1./w)*sin(w*(i-1)*dt)*(E11 +E22*cos(w*(i-1)*dt + theta));
%========================================================
x(i+1,j) = x(i-1,j) + 2.*v(i,j)*dt + eps(i,j)*dt;