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Uniform Distribution of Eigenstates on a Torus with Two Point Scatterers

2016/06/22 by Yesha, Nadav
#Analysis of PDEs (math.AP) #Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1606.07053

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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