Universal spectral statistics of Andreev billiards: semiclassical approach

TL;DR

This paper provides a semiclassical interpretation of spectral form factors in superconducting-normal hybrid systems, extending the understanding of universality classes in random-matrix theory beyond traditional ensembles.

Contribution

It introduces a semiclassical approach to analyze spectral statistics in Andreev billiards and quantum graphs, linking them to extended universality classes.

Findings

Semiclassical interpretation of spectral form factors for Andreev billiards.

Extension of universality classes in random-matrix theory to hybrid systems.

Application to quantum graphs and Andreev billiards.

Abstract

The classification of universality classes of random-matrix theory has recently been extended beyond the Wigner-Dyson ensembles. Several of the novel ensembles can be discussed naturally in the context of superconducting-normal hybrid systems. In this paper, we give a semiclassical interpretation of their spectral form factors for both quantum graphs and Andreev billiards.