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Open Quantum Systems Decoherence Quantum Simulation

Degeneracies In a Weighted Sum of Two Squares

arXiv
Authors: Ishan Vinayagam Ramesh, Maxim Olshanii

Year

2024

Paper ID

37324

Status

Preprint

Abstract Read

~2 min

Abstract Words

103

Citations

N/A

Abstract

This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, 3n12+n22, 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.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, 3n1^2+n2^2, can be realized in more than one way.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2411.02436 [2] arXiv https://arxiv.org/abs/2411.02436 [3] Publisher https://arxiv.org/abs/2411.02436

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