Quantum Andreev map: A paradigm of quantum chaos in superconductivity

TL;DR

This paper introduces quantum Andreev maps as a computationally efficient model to study quantum chaos in superconductivity, enabling testing of theoretical predictions related to excitation gaps and universal distributions.

Contribution

The authors develop quantum maps incorporating Andreev reflection and symmetry, providing a new tool for analyzing quantum chaos in superconducting systems.

Findings

Universal distribution of excitation gap observed for large Lyapunov exponent

Logarithmic reduction of the gap when Ehrenfest time approaches quasiparticle dwell time

Quantum Andreev maps are more efficient than billiard models for simulations

Abstract

We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.