On the magnetic Dirichlet to Neumann operator on the disk -- strong diamagnetism and strong magnetic field limit--

TL;DR

This paper investigates the behavior of the magnetic Dirichlet-to-Neumann operator on a disk, demonstrating that its ground state energy diverges as the magnetic field increases, which advances understanding of magnetic effects in quantum systems.

Contribution

It provides a rigorous analysis confirming the conjecture that the ground state energy tends to infinity with increasing magnetic field on the disk.

Findings

Ground state energy tends to +∞ as magnetic field increases

Supports analysis of curvature effects in general domains

Advances understanding of magnetic diamagnetism in quantum operators

Abstract

Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator on the disk tends to $+\infty$ as the magnetic field tends to $+\infty$. This is an important step towards the analysis of the curvature effect in the case of general domains in $\mathbb R^2$.