A personal project that grew out of analyzing spontaneous simultaneity using statistical methods in Abelian Sandpiles.
After that, I moved to using Random Matrix Theory (RMT) to analyze the Model to see the statistical behaviour as it approached and went beyond the critical points. I plotted the evolution of Eigenvalue deviation (standard deviation of eigenvalues) vs Lattice Size to see how the general behavior of the system was changing (as Lattice Size changed) along with plotting the mean (of Eigenvalues) vs Lattic Size as well, after establishing the graph matched Wigner's distribution.
Then I introduced some physical models in the general model. (in my system it is a 2D Pendulum; adjusted for large oscillations as well) I did not expect to see any significantly different results as the general model I plotted is for a GOE and the pendulum is a case for a GOE.
I am working on the theoretical models, I have come across and worked with the math required for this but I think the exact solution has, until now, only been approximated, as a chaotic system, or a symmetry breaking implies going from one kind of an ensemble to another. (in this case GOE to GUE) I also have not seen anyone (or any literature) plot eigenvalue deviations (or mean) as a measure of the statistical evolution of the system, so I will have to work on that myself.
In the repo, you'll also find a brief description (the pdf) of the work I did during my internship where I was introduced to RMT, about a year before I took on this project.