Localised eigenfunctions in Seba billiards

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.

23 pages, 1 figure

References in corpus (1)

• Quantum unique ergodicity for SL_2(Z)\H

Cited by in corpus (9)

• Statistics of wave functions for a point scatterer on the torus
• Quantum Chaos for point scatterers on flat tori
• Scarred eigenstates for arithmetic toral point scatterers
• Localization of low-energy eigenfunctions in Seba billiards
• Superscars for Arithmetic Point Scatterers II
• Quantum Ergodicity for Point Scatterers on Arithmetic Tori
• Superscars in the Seba billiard
• Finite deficiency indices and uniform remainder in Weyl's law
• Eigenvalues of Šeba billiards with localization of low-energy eigenfunctions