Diamagnetism versus Robin condition and concentration of ground states

TL;DR

This paper investigates how Robin boundary conditions influence the ground state energy of the magnetic Laplacian, showing that they weaken diamagnetism and cause ground states to concentrate near boundary points of maximal curvature.

Contribution

It provides the first asymptotic analysis demonstrating Robin conditions weaken diamagnetism and describes ground state concentration near boundary points of maximal curvature.

Findings

Robin condition weakens diamagnetism

Ground states concentrate near boundary points of maximal curvature

Magnetic field does not affect the two-term expansion in a special limit

Abstract

We estimate the ground state energy for the magnetic Laplacian with a Robin condition. In a special asymptotic limit, we find that the magnetic field does not contribute to the two-term expansion of the ground state energy, thereby proving that the Robin condition weakens diamagnetism. We discuss a semi-classical version of the operator and prove that the ground states concentrate near the boundary points of maximal curvature.