Index a matrix multiplied by a time dependent function

Hi there,

I'm trying to index a matrix that's multiplied by a time dependent function, but keep getting the error "inner dimensions must agree" in the U expression line. I need to know the exact matrix values for each interaction related to the function E(t) in the time, i.e., U(1) related to E(1) and so on. Thanks in advance!

Here's the code

%% Quantum Control

format long
clear all
clc

%% Variables

        fs=10;
        ft = -20000:1/fs:20000; % Time            
        alpha = 0.001; % Time parameter   
        beta = 0.001; % Time parameter
        ai = 0.2; % Pop |1>
        ai2 = 0.8; % Pop |2>
        af = 1; % Pop Final |1>        
        w0 = 0.02; % w0 = (E2 - E1)/h        
        mi = 6; % Dipole
        phii = pi/24; % Relative phase
        phif = pi/4; % Relative phase final
        E1 = 1; % Energy
        E2 = 2; % Energy 2
        H = [0 1;1 0]; % Interaction hamiltonian
        H0 = [E1 0;0 E2]; % Matriz do Hamiltoniano sem Interação

%% Control function

        g = 1./(1+exp(-alpha.*ft));
        f = ai*(1-g)+af*g;
        p = 1./(1+exp(-beta.*ft));
        h = phii*(1-p)+phif*p;
        
%% Electric field 

        E = alpha.*(af-ai).*exp(alpha.*ft).*sin(w0.*ft+h)./(mi.*(1+exp(alpha.*ft)).*sqrt((1-ai+(1-af).*exp(alpha.*ft)).*(ai+af.*exp(alpha.*ft))))+2.*beta.*(phif-phii).*exp(beta.*ft).*sqrt(f.*(1-f)).*cos(w0.*ft+h)/(mi.*(1-2.*f).*(1+exp(beta.*ft).^2));
    
%% Time evolution operator

        [V, D]=eig(H);

        Z = expm(H0);

        Z1 = expm(D);
        
        U = exp(-1i.*ft./2).*Z.*exp(1i.*mi.*E.*ft).*V.*Z1.*inv(V).*exp(-1i.*ft./2).*Z;
    
%% End

[Walter Roberson]

V.*Z1.*inv(V) is probably a mistake. Any multiplication of a matrix and its inverse should be using * instead of .*

You should likely also be coding using Z1/V instead of Z1.*inv(V)

In your long expression you have a / that should probably be ./

[guilherme stahlberg]

I've tried either * or .* but keep getting the same error "inner dimensions must agree". Same regarding the / and./

Answer 1

[KSSV]

U = zeros(2,2,length(ft)) ; 
for i = 1:length(ft)
        U(:,:,i) = exp(-1i.*ft(i)./2).*Z.*exp(1i.*mi.*E(i).*ft(i)).*V.*Z1.*inv(V).*exp(-1i.*ft(i)./2).*Z;
end

[Walter Roberson]

This is likely to be mathematical nonsense though. V.*Z1.*inv(V) is much more likely to need V*Z1*inv(V) or similar.