Asymptotic spectral analysis in colliding leaky quantum layers

TL;DR

This paper studies the spectral behavior of a Schroedinger operator with complex delta interactions supported on two parallel hypersurfaces as their separation approaches zero, establishing convergence and eigenvalue corrections.

Contribution

It provides the first rigorous analysis of the spectral limit and eigenvalue corrections for colliding leaky quantum layers in any dimension.

Findings

Norm-resolvent convergence to a limiting operator

First-order eigenvalue corrections derived

Applicable to hypersurfaces in any Euclidean dimension

Abstract

We consider the Schroedinger operator with a complex delta interaction supported by two parallel hypersurfaces in the Euclidean space of any dimension. We analyse spectral properties of the system in the limit when the distance between the hypersurfaces tends to zero. We establish the norm-resolvent convergence to a limiting operator and derive first-order corrections for the corresponding eigenvalues.