Uniform distribution of eigenstates on a torus with two point scatterers

Nadav Yesha

doi:10.4171/JST/233

Uniform distribution of eigenstates on a torus with two point scatterers

Nadav Yesha

Department of Mathematics

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

Abstract

We study the Laplacian perturbed by two delta potentials on a two-dimensional flat torus. There are two types of eigenfunctions for this operator: old, or unperturbed eigenfunctions which are eigenfunctions of the standard Laplacian, and new, perturbed eigenfunctions which are affected by the scatterers. We prove that along a density one sequence, the new eigenfunctions are uniformly distributed in configuration space, provided that the difference of the scattering points is Diophantine.

Original language	English
Pages (from-to)	1509-1527
Number of pages	19
Journal	Journal of Spectral Theory
Volume	8
Issue number	4
DOIs	https://doi.org/10.4171/JST/233
State	Published - 2018

Bibliographical note

Publisher Copyright:
© European Mathematical Society

Keywords

Primary: 35P20
Secondary: 81Q50

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Geometry and Topology

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10.4171/JST/233

Cite this

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abstract = "We study the Laplacian perturbed by two delta potentials on a two-dimensional flat torus. There are two types of eigenfunctions for this operator: old, or unperturbed eigenfunctions which are eigenfunctions of the standard Laplacian, and new, perturbed eigenfunctions which are affected by the scatterers. We prove that along a density one sequence, the new eigenfunctions are uniformly distributed in configuration space, provided that the difference of the scattering points is Diophantine.",

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AB - We study the Laplacian perturbed by two delta potentials on a two-dimensional flat torus. There are two types of eigenfunctions for this operator: old, or unperturbed eigenfunctions which are eigenfunctions of the standard Laplacian, and new, perturbed eigenfunctions which are affected by the scatterers. We prove that along a density one sequence, the new eigenfunctions are uniformly distributed in configuration space, provided that the difference of the scattering points is Diophantine.

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KW - Secondary: 81Q50

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Uniform distribution of eigenstates on a torus with two point scatterers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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