Spectral Statistics Beyond Random Matrix Theory

TL;DR

This paper investigates the spectral correlations in weakly disordered metallic grains beyond traditional random matrix theory, revealing nonuniversal behaviors influenced by grain shape and conductance.

Contribution

It introduces a nonperturbative method to analyze large frequency asymptotics of spectral correlators, extending understanding beyond standard random matrix results.

Findings

Singularities in spectral correlations are smoothed out in finite conductance grains.

Spectral statistics depend on grain shape and conductance, indicating nonuniversality.

Results suggest a broader applicability to systems with finite Heisenberg time.

Abstract

Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the Heisenberg time. We find that the singularities (present for random matrix ensembles) are washed out in a grain with a finite conductance. The results are nonuniversal (they depend on the shape of the grain and on its conductance), though they suggest a generalization for any system with finite Heisenberg time.