Uniform distribution of eigenstates on a torus with two point scatterers

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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 languageEnglish
Pages (from-to)1509-1527
Number of pages19
JournalJournal of Spectral Theory
Issue number4
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© European Mathematical Society


  • Primary: 35P20
  • Secondary: 81Q50

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology


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