Quantum-classical correspondence in the wavefunctions of Andreev billiards

TL;DR

This paper investigates the classical and quantum wavefunctions of chaotic Andreev billiards, revealing complex phenomena like wavefunction scarring and localization due to mixed classical dynamics, challenging common approximations.

Contribution

It provides a detailed analysis of wavefunction behavior in chaotic Andreev billiards, highlighting the limitations of the retracing approximation and uncovering new wave phenomena.

Findings

Classical dynamics are generally mixed, not purely chaotic or regular.

Wavefunctions exhibit phenomena such as periodic orbit scarring.

Localization occurs on classical phase space structures like tori and intermittent regions.

Abstract

We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that in general the classical dynamics of these normal-superconductor hybrid systems is mixed, thereby indicating the limitations of a widely used retracing approximation. We show that the mixed classical dynamics gives rise to a wealth of wavefunction phenomena, including periodic orbit scarring and localization of the wavefunction onto other classical phase space objects such as intermittent regions and quantized tori.