Strong diamagnetism for the ball in three dimensions

TL;DR

This paper derives an asymptotic formula for the lowest eigenvalue of a magnetic Schrödinger operator in a 3D ball with Neumann boundary conditions, showing it increases monotonically with magnetic field strength.

Contribution

It provides a detailed asymptotic analysis of the eigenvalue and proves its monotonicity for large magnetic fields, advancing understanding of magnetic quantum systems.

Findings

Eigenvalue asymptotics derived for large magnetic fields

Monotonic increase of eigenvalue established

Enhanced understanding of magnetic Schrödinger operators in 3D domains

Abstract

In this paper we give a detailed asymptotic formula for the lowest eigenvalue of the magnetic Neumann Schr\"odinger operator in the ball in three dimensions with constant magnetic field, as the strength of the magnetic field tends to infinity. This asymptotic formula is used to prove that the eigenvalue is monotonically increasing for large values of the magnetic field.