Effective Random Matrix Theory description of chaotic Andreev billiards

TL;DR

This paper develops an effective random matrix theory for chaotic Andreev billiards, accurately describing gap fluctuations and density of states, and compares well with numerical results, revealing a linear gap decrease with Ehrenfest time.

Contribution

It introduces an effective RMT approach for finite Ehrenfest time in chaotic Andreev billiards, matching numerical data and providing semi-classical interpretation.

Findings

Good agreement with numerical calculations for Sinai-Andreev billiards.

Linear decrease of the mean field gap with Ehrenfest time.

Semi-classical interpretation of the density of states tail.

Abstract

An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the numerical calculation for Sinai-Andreev billiards. A systematic linear decrease of the mean field gap with increasing Ehrenfest time $\tau_E$ is observed but its derivative with respect to $\tau_E$ is in between two competing theoretical predictions and close to that of the recent numerical calculations for Andreev map. The exponential tail of the density of states is interpreted semi-classically.