Emergence of Quantum Ergodicity in Rough Billiards

TL;DR

This paper introduces a new regime of quantum ergodicity in rough billiards, showing that eigenstates can be extended yet peaked, with implications for level statistics and a mapping to band random matrix models.

Contribution

It analytically maps rough billiards to band random matrix models, revealing a novel ergodic regime with extended but peaked eigenstates.

Findings

Identification of a new ergodic regime in rough billiards.

Eigenstates are extended over energy surface but have peaked structures.

Numerical simulations support the analytical results.

Abstract

By analytical mapping of the eigenvalue problem in rough billiards on to a band random matrix model a new regime of Wigner ergodicity is found. There the eigenstates are extended over the whole energy surface but have a strongly peaked structure. The results of numerical simulations and implications for level statistics are also discussed.