# Estimates for eigenvalues of Aharonov-Bohm operators with varying poles and non-half-interger circulation

## TL;DR

This paper analyzes how the eigenvalues of Aharonov-Bohm operators change as the pole moves within a domain, providing estimates and detailed blow-up analysis for non-half-integer circulations.

## Contribution

It introduces new estimates for eigenvalue variation and a precise blow-up analysis for eigenfunctions with non-half-integer circulation.

## Key findings

- Eigenvalue variation rate depends on eigenfunction vanishing order.
- Sharp convergence estimates for scaled eigenfunctions.
- Detailed blow-up analysis for eigenfunctions near the pole.

## Abstract

We study the behavior of eigenvalues of a magnetic Aharonov-Bohm operator with non-half-integer circulation and Dirichlet boundary conditions in a planar domain. As the pole is moving in the interior of the domain, we estimate the rate of the eigenvalue variation in terms of the vanishing order of the limit eigenfunction at the limit pole. We also provide an accurate blow-up analysis for scaled eigenfunctions and prove a sharp estimate for their rate of convergence.