Uniform spectral estimates for families of Schrodinger operators with magnetic field of constant intensity and applications

TL;DR

This paper derives uniform spectral estimates for the Neumann realization of magnetic Schrödinger operators with constant magnetic field intensity, relevant to liquid crystals and superconductivity in large domains.

Contribution

It provides new uniform estimates for the spectrum's bottom of magnetic Schrödinger operators with constant magnetic field, applicable to physical models.

Findings

Established uniform spectral bounds for large magnetic field strengths.

Applied results to liquid crystal and superconductivity models.

Enhanced understanding of spectral behavior in magnetic quantum systems.

Abstract

The aim of this paper is to establish uniform estimates of the spectrum's bottom of the Neumann realization of $(i\nabla+q\A)^2$ on a bounded open set $\Om$ with smooth boundary when $|\nabla\times\A|=1$ and $q\to+\infty$. This problem was motivated by a question occuring in the theory of liquid crystals and appears also in superconductivity questions in large domains.