Discrete spectrum from local perturbations of leaky curves

TL;DR

This paper investigates how local perturbations of leaky curves with periodic shapes can create discrete spectral values below the continuum threshold, even when these perturbations have zero mean.

Contribution

It demonstrates that local perturbations of leaky curves can induce discrete spectrum below the continuum, expanding understanding of spectral properties in such models.

Findings

Local perturbations can generate discrete spectrum below the continuum threshold.

Zero mean perturbations can still produce bound states.

Periodic shape of the support influences spectral properties.

Abstract

We discuss spectrum of a class of singular Schr\"odinger operator models known as leaky curves and show that if the interaction support has a periodic shape, its local perturbations can give rise to a discrete spectrum below the continuum threshold even if they are of `zero mean'.