Localised eigenfunctions in Seba billiards

TL;DR

This paper introduces new quasimodes for the Laplacian with a delta potential and demonstrates eigenfunction localization in Seba billiards, revealing insights into spectral perturbations and eigenfunction behavior.

Contribution

It presents novel families of quasimodes for Laplacians with delta potentials and shows eigenfunction localization in Seba billiards under certain spectral conditions.

Findings

Existence of new quasimodes for Laplacian with delta potential

Eigenfunctions localize around unperturbed eigenfunctions in Seba billiards

Spectral conditions influence eigenfunction localization

Abstract

We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Seba billiards that localise around a pair of unperturbed eigenfunctions.