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clear all
clc
b11=0;b12=0;b13=1;b21=0.5;b22=0.5;b23=1.5;b4=0.5;b5=2;b6=2;b7=0.2;b8=0.005;y=[0 -1i;1i 0];
a0=[1 0 0 0 ];a1=[0 1 0 0 ];a2=[0 0 1 0 ];a3=[0 0 0 1 ];a00=a0'*a0;a11=a1'*a1;a22=a2'*a2;a33=a3'*a3;a12=a1'*a2;a21=a12';a23=a2'*a3;a32=a23';
a111=-a00+a11-a22-a33;a222=-a00-a11+a22-a33;a333=-a00-a11-a22+a33;a123=a12+a21+a23+a32;a4=b21*a111+b22*a222+b23*a333;

t_max=30;
n_max=1000;
% l_max=100;
rho(:,:,n_max)=zeros(4);
psy1=[0 1 0 0]';
% psy1=[0 1/sqrt(2) 1/sqrt(2) 0]';
rho(:,:,1)=psy1*psy1';
h=t_max/n_max;
% format long
for b3=10:0.1:10.9
for n=1:n_max
        k=rho(:,:,n);t=(n-1)*h;
        b111=0.5*b11-2*b21*b3*b4*sin(b5*t);b222=0.5*b12-2*b22*b3*b4*sin(b5*t);b333=0.5*b13-2*b23*b3*b4*sin(b5*t);
        H1=b111*a111+b222*a222+b333*a333+b6*a123-1i*b7*a33;
        k1=1i*(k*H1-H1*k)+4*b8*(a4*k*a4-0.5*a4*a4*k-0.5*k*a4*a4);
        k=rho(:,:,n)+h/2*k1;s=t+1/2*h;
        b111=0.5*b11-2*b21*b3*b4*sin(b5*s);b222=0.5*b12-2*b22*b3*b4*sin(b5*s);b333=0.5*b13-2*b23*b3*b4*sin(b5*s);
        H1=b111*a111+b222*a222+b333*a333+b6*a123-1i*b7*a33;
        k2=1i*(k*H1-H1*k)+4*b8*(a4*k*a4-0.5*a4*a4*k-0.5*k*a4*a4);
        k=rho(:,:,n)+h/2*k2;
        k3=1i*(k*H1-H1*k)+4*b8*(a4*k*a4-0.5*a4*a4*k-0.5*k*a4*a4);
        k=rho(:,:,n)+h*k3;s=t+h;
        b111=0.5*b11-2*b21*b3*b4*sin(b5*s);b222=0.5*b12-2*b22*b3*b4*sin(b5*s);b333=0.5*b13-2*b23*b3*b4*sin(b5*s);
        H1=b111*a111+b222*a222+b333*a333+b6*a123-1i*b7*a33;
        k4=1i*(k*H1-H1*k)+4*b8*(a4*k*a4-0.5*a4*a4*k-0.5*k*a4*a4);
        rho(:,:,n+1)=rho(:,:,n)+h/6*(k1+2*k2+2*k3+k4);
        c(n)=real(rho(4,4,n));
end
s=0.012*sum (c)
end
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