Small gaps in the spectrum of tori: asymptotic formulae

TL;DR

This paper derives an asymptotic formula for counting small gaps between the first N Laplacian eigenvalues on almost all flat tori, valid down to the Planck scale, advancing understanding of spectral gap distribution.

Contribution

It provides a new asymptotic formula for small spectral gaps on almost all flat tori, extending previous results to the Planck scale.

Findings

Asymptotic formula valid down to the Planck scale

Applicable to almost all flat and rectangular tori

Advances spectral gap distribution understanding

Abstract

We establish an asymptotic formula, uniformly down to the Planck scale, for the number of small gaps between the first N eigenvalues of the Laplacian on almost all flat tori and also on almost all rectangular flat tori.