Almost all eigenfunctions of a rational polygon are uniformly distributed

Jens Marklof; Zeév Rudnick

doi:10.4171/JST/23

Almost all eigenfunctions of a rational polygon are uniformly distributed

Jens Marklof, Zeév Rudnick

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability measures. We prove that this sequence contains a density-one subsequence that converges to Lebesgue measure.

Original language	English
Pages (from-to)	107-113
Number of pages	7
Journal	Journal of Spectral Theory
Volume	2
Issue number	1
DOIs	https://doi.org/10.4171/JST/23
State	Published - 2012

Keywords

Billiards in rational polygons
Pseudo-integrable systems
Quantum ergodicity

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Geometry and Topology

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10.4171/JST/23

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title = "Almost all eigenfunctions of a rational polygon are uniformly distributed",

abstract = "We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability measures. We prove that this sequence contains a density-one subsequence that converges to Lebesgue measure.",

keywords = "Billiards in rational polygons, Pseudo-integrable systems, Quantum ergodicity",

author = "Jens Marklof and Ze{\'e}v Rudnick",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2012",

doi = "10.4171/JST/23",

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AU - Marklof, Jens

AU - Rudnick, Zeév

N1 - Publisher Copyright: © European Mathematical Society.

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AB - We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability measures. We prove that this sequence contains a density-one subsequence that converges to Lebesgue measure.

KW - Billiards in rational polygons

KW - Pseudo-integrable systems

KW - Quantum ergodicity

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DO - 10.4171/JST/23

M3 - مقالة

SN - 1664-039X

VL - 2

SP - 107

EP - 113

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 1

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Almost all eigenfunctions of a rational polygon are uniformly distributed

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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