Spectral correlations: understanding oscillatory contributions

TL;DR

This paper provides a clear derivation of a spectral correlation relation, demonstrating its broader applicability beyond random matrix theory and clarifying its consistency with previous models without needing resurgence.

Contribution

It offers a transparent derivation of a spectral correlation relation, extending its validity beyond random matrix theory and resolving apparent contradictions in earlier perspectives.

Findings

The relation connects smooth and oscillatory spectral components.

The result is applicable beyond random matrix models.

No resurgence concept is necessary for the interpretation.

Abstract

We give a transparent derivation of a relation obtained using a supersymmetric non-linear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902, (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models. In particular, the concept of resurgence is not required.