Counterexample to strong diamagnetism for the magnetic Robin Laplacian

TL;DR

This paper presents a counterexample to the strong diamagnetism phenomenon in the magnetic Robin Laplacian, showing that under certain boundary conditions, the expected magnetic behavior does not hold.

Contribution

It provides the first explicit counterexample to strong diamagnetism for the magnetic Robin Laplacian in a unit disc with uniform magnetic field.

Findings

Counterexample to strong diamagnetism established

Asymptotic analysis of lowest eigenvalue as Robin parameter tends to -∞

Demonstrates boundary condition effects on magnetic spectral properties

Abstract

We determine a counterexample to strong diamagnetism for the Laplace operator in the unit disc with a uniform magnetic field and Robin boundary condition. The example follows from the accurate asymptotics of the lowest eigenvalue when the Robin parameter tends to $-\infty$.