Dear Community,
I am trying to figure out what is happening in this article (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.29.130) when they are calculating the Fredholm Determinant (Section IV). The basic idea is that you want to solve
$$
k = |\frac{det(1+h_0)}{det'(1+h_0+v)}|
$$...
Yeah, But using Matlab it takes me around 10 min to do 3 iteration with m=20 and n=10. I am also doing it the brute force, with an script like this:
clear all, clc
alpha = 1;
Theta = 0.1;
f(n) = exp(-n);
for o = 1:4;
for i = 1:20; %first sum
p(i) = 2*f(i+n)*f(i);
end
q(n) =...
Perfect, that is just a hell of a calculation to perform, as we have for m=256 then 128 etc, means that we will end up with an equation that is super big after a few iterations.
okay, but when you write the program is the general idea then
1. set limit in the infinity sum to (lets say) 500 and the sum with n to 50, so from the first sum we get something like R(n+1)R(1)... and from the second something like R(n-1)r(1)...R(n-50)R(50),,,
2. You then get a function R_n...
I did understand that, I am trying to write the computer program. My problem is with the second sum, that has the limit n. This limit would change all the time... for small n, it is small for large n it is large, but can not see how I can implement this limit, in example MATLAB without...
So just to clarify the method, as I seem to have some problems with it. If we choose a=1, k=1, so our trial function is R_n = exp(-n). Then in order to implement your results I have to choose a value for n. Choosing n=2 and calculating the sums gives us a number. Which cannot be put back into...
okay, that might work. My only problem with that is that it gives us an equation for R_n, but the sum requires us to also use R_(n+1), these could/have different coefficients then R_n.
Do you imply that I should only have one A and n constant or one for every R_n, (n=1,2,...).
So I set the infinity sum to a fix number, let's say 10. Is the idea then to;
1. set the function F_n = f_n*exp(-n)
2. Isolate the constant for f_n as a value of higher order constant f_(n+1), f_(n+2) etc
3. Insert it into F_(n+1)
4. Isolation f_(n+1) as a function of f_(n+2) etc and so on
5. At...
Hey Guys, Trying to figure out how to replicate the following from an article, but can not understand their notations;
The main points are:
The bounce action can be written as the equation
$$\left( n^2 \Theta^2 + 2\alpha n\Theta -1\right)R_n = 2 \sum_{m=1}^\infty R_{n+m}R_m + \sum_{m=1}^n...
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