Degeneracies In a Weighted Sum of Two Squares
Mathematical Physics
2025-04-02 v2 Quantum Gases
math.MP
Quantum Physics
Abstract
This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, , can be realized in more than one way. Our project was inspired by a particular study of two-dimensional quantum billiards [S. G. Jackson, H. Perrin, G. E. Astrakharchik, and M. Olshanii, SciPost Phys. Core 7, 062 (2024)] where the weighted sums of interest represents an energy level with the two integers being the billiard's quantum numbers; there, the 3-fold degeneracies seem to dominate the energy spectrum. Interestingly, contrary to the conventional paradigm, these degeneracies are not caused by some non-commuting symmetries of the system.
Keywords
Cite
@article{arxiv.2411.02436,
title = {Degeneracies In a Weighted Sum of Two Squares},
author = {Ishan Vinayagam Ramesh and Maxim Olshanii},
journal= {arXiv preprint arXiv:2411.02436},
year = {2025}
}