Small Scale Equidistribution for a Point Scatterer on the Torus

Nadav Yesha

doi:10.1007/s00220-019-03669-0

Small Scale Equidistribution for a Point Scatterer on the Torus

Nadav Yesha

Department of Mathematics

University of Haifa

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

Abstract

We study the small scale distribution of the eigenfunctions of a point scatterer (the Laplacian perturbed by a delta potential) on two- and three-dimensional flat tori. In two dimensions, we establish small scale equidistribution for the “new” eigenfunctions holding all the way down to the Planck scale. In three dimensions, small scale equidistribution is established for all of the “new” eigenfunctions at certain scales.

Original language	American English
Pages (from-to)	199-224
Number of pages	26
Journal	Communications in Mathematical Physics
Volume	377
Issue number	1
DOIs	https://doi.org/10.1007/s00220-019-03669-0
State	Published - 1 Jul 2020

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We study the small scale distribution of the eigenfunctions of a point scatterer (the Laplacian perturbed by a delta potential) on two- and three-dimensional flat tori. In two dimensions, we establish small scale equidistribution for the “new” eigenfunctions holding all the way down to the Planck scale. In three dimensions, small scale equidistribution is established for all of the “new” eigenfunctions at certain scales.",

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AB - We study the small scale distribution of the eigenfunctions of a point scatterer (the Laplacian perturbed by a delta potential) on two- and three-dimensional flat tori. In two dimensions, we establish small scale equidistribution for the “new” eigenfunctions holding all the way down to the Planck scale. In three dimensions, small scale equidistribution is established for all of the “new” eigenfunctions at certain scales.

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Small Scale Equidistribution for a Point Scatterer on the Torus

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