On Aharonov-Bohm operators with two colliding poles

TL;DR

This paper investigates the spectral behavior of Aharonov-Bohm operators with two poles as they approach each other at an interior point, providing precise asymptotic descriptions of eigenvalues.

Contribution

It establishes sharp asymptotic formulas for eigenvalues of Aharonov-Bohm operators with two colliding poles, advancing understanding of their spectral properties.

Findings

Derived sharp asymptotics for eigenvalues as poles collide

Identified the influence of pole collision on spectral behavior

Provided mathematical characterization of eigenvalue limits

Abstract

We consider Aharonov-Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction.