Eigenfunctions for partially rectangular billiards

TL;DR

This paper explores the eigenfunctions of billiard systems with rectangular parts using a 'black box' approach, covering various complex billiards like Bunimovich, Sinai, and pseudointegrable types.

Contribution

It extends the 'black box' method to analyze eigenfunctions in billiards with rectangular components, providing new insights into their spectral properties.

Findings

Eigenfunctions exhibit specific localization patterns.

The method applies to a range of complex billiard shapes.

Results suggest new spectral invariants for these systems.

Abstract

In this note we further develop the idea of using a ``black box'' point of view (see our previous work) to study eigenfunctions for billiards which have rectangular components: they include the Bunimovich billiard, the Sinai billiard, and the recently popular pseudointegrable billiards