Eigenvalue estimates for the Aharonov-Bohm operator in a domain

TL;DR

This paper provides semi-classical eigenvalue estimates for the Aharonov-Bohm operator in bounded domains, presents a counterexample to a proposed inequality, and supports findings with numerical analysis.

Contribution

It introduces new semi-classical bounds for eigenvalues and challenges a previously conjectured inequality in the context of the Aharonov-Bohm operator.

Findings

Semi-classical estimates for eigenvalues established

Counterexample to the generalized diamagnetic inequality provided

Numerical studies support theoretical results

Abstract

We prove semi-classical estimates on moments of eigenvalues of the Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present a counterexample to the generalized diamagnetic inequality which was proposed by Erdos, Loss and Vougalter. Numerical studies complement these results.