Percival's conjecture for the Bunimovich mushroom billiard

Sean Patrick Gomes*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

The Laplace-Beltrami eigenfunctions on a compact Riemannian manifold M whose geodesic billiard flow has mixed character have been conjectured by Percival to split into two complementary families, with all semiclassical mass supported in the completely integrable and ergodic regions of phase space respectively. In this paper, we consider the Dirichlet Laplacian on a family of mushroom billiards M t parametrised by the length of their rectangular component. We prove that there exist eigenfunction subsequences of M t with full upper density that split as conjectured by Percival for almost all , providing the first example of a billiard known to satisfy this weak form of Percival's conjecture.

Original languageEnglish (US)
Pages (from-to)4108-4136
Number of pages29
JournalNonlinearity
Volume31
Issue number9
DOIs
StatePublished - Jul 26 2018

Keywords

  • Percival's conjecture
  • Quantum ergodicity
  • mushroom billiard
  • quantum chaos

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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