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Journal of Spectral Theory

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Volume 8, Issue 4, 2018, pp. 1509–1527
DOI: 10.4171/JST/233

Published online: 2018-10-22

Uniform distribution of eigenstates on a torus with two point scatterers

Nadav Yesha[1]

(1) University of Bristol, UK and University of Haifa, Israel

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.

Keywords: Point scatterers, quantum ergodicity, flat torus

Yesha Nadav: Uniform distribution of eigenstates on a torus with two point scatterers. J. Spectr. Theory 8 (2018), 1509-1527. doi: 10.4171/JST/233