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sampleInput.m
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%% Bearing in mind the effort that went into the development of FeynDyn,
%% the author would indeed appreciate if users can please cite:
%% 1) The paper: N. Dattani (2013) Comp. Phys. Comm. Volume 184, Issue 12, Pg. 2828-2833 , and
%% 2) The code: N. Dattani (2013) FeynDyn. http://dx.doi.org/10.6084/m9.figshare.823549
%% To make sure your code is the most updated version, please e-mail [email protected]
%% Bug reports, suggestions, and requests for extensions are more than encouraged: [email protected]
%% This program is protected by copyright law. Nike S. Dattani , 13/8/12
%% This sample input file, upon pressing F5, plots the real and imaginary parts of <i|rho|j> as a function
% of time for the hamiltonian presented in Comp. Phys. Comm. Volume 184, Issue 12, Pg. 2828-2833
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 1. fundamental constants
kb=1.3806504*10^(-23); % Joules / Kelvin
hbar=1.054571628*10^(-34); % Joule * seconds
%% 2. temperature
temperature=25;
beta=1/(kb*temperature);
%% 3. system hamiltonian
Omega=hbar*1e12*pi/8; % Rabi frequency in Joules
H=[0 Omega/2; Omega/2 0]; % System hamiltonian in Joules
%% 4. initial denisty matrix
rhoInitial=[0 0; 0 1];
%% 5. system coupling matrix
systemCouplingMatrix=[0 0;0 1]; % The system is coupled to the bath via |1X1|
%systemCouplingMatrix=[1 0;0 -1]; % The system is coupled to the bath via sigma_z
%% 6. spectral distribution function
alpha=0.027*pi; % prefactor. In ps^2 / rad^2
wc=2.2; % cutoff frequency. In rad/ps
dw=0.01; % stepsize for w in J(w). In rad/ps
w=dw:dw:14; % must start with dw because coth(0)=infinity. In rad/ps
J=alpha*exp(-(w/wc).^2).*w.^3;% spectral density. In rad/ps
J=J*1e12*hbar; % spectral distribution function. In Joules
w=w*1e12; % w in s-1
dw=dw*1e12; % dw in s-1
%% 7. numerical parameters for Feynman integral
deltaKmax=9; % number of time steps before memory kernel dies
totalT=10/1e12; % total time for the simulation, in seconds
dt=33/totalT; % size of time step (delta t)
finalPoint=round(dt*totalT); % number of timesteps in total
allPointsORjustFinalPoint='allPoints'; % do you just want the density matrix at time=totalT ? or do you want it at every point until then
cpuORgpu='cpu';
%% 8. build input array that represents the densitry matrix (flattened to a column vector) as a function of time (where the columns represent the time steps)
rho=zeros(numel(H),finalPoint+1);
rho(:,1)=reshape(rhoInitial.',[],1); % I'm not sure about the transpose, since I'm not sure about labeling of the states in the column vector for the purposes of the final sum function.
%% 9. run the program and plot only <0|rho|0> and <1|rho|1> as a function of time
wholeDensityMatrixOrJustDiagonals='justDiagonals';
[rho_onlyDiagonals,elapsedTime_onlyDiagonals]=FeynDyn(finalPoint,deltaKmax,totalT,rho,H,systemCouplingMatrix,w,dw,J,temperature,wholeDensityMatrixOrJustDiagonals,allPointsORjustFinalPoint,cpuORgpu);
figure(1);hold('on')
plot(0:totalT/finalPoint:totalT,real(rho_onlyDiagonals(1,:)));
plot(0:totalT/finalPoint:totalT,real(rho_onlyDiagonals(4,:)));
xlabel('time (seconds)');
%% 10. run the program and plot all elements of the density matrix as a function of time
wholeDensityMatrixOrJustDiagonals='wholeDensityMatrix';
[rho_allElements,elapsedTime_allElements]=FeynDyn(finalPoint,deltaKmax,totalT,rho,H,systemCouplingMatrix,w,dw,J,temperature,wholeDensityMatrixOrJustDiagonals,allPointsORjustFinalPoint,cpuORgpu);
figure(2);hold('on')
plot(0:totalT/finalPoint:totalT,real(rho_allElements(1,:)));
plot(0:totalT/finalPoint:totalT,real(rho_allElements(3,:)),'r');plot(0:totalT/finalPoint:totalT,imag(rho_allElements(3,:)),'--r');
plot(0:totalT/finalPoint:totalT,real(rho_allElements(3,:)),'r');plot(0:totalT/finalPoint:totalT,-imag(rho_allElements(3,:)),'--r');
plot(0:totalT/finalPoint:totalT,real(rho_allElements(4,:)));
xlabel('time (seconds)');