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

Abstract

The aim of this paper is to establish uniform estimates of the bottom of the spectrum of the Neumann realization of (ð’¾âˆ‡ + qA)² on a bounded open set Ω with smooth boundary when |∇ × A| = 1 and q → +∞. This problem was motivated by a question occurring in the theory of liquid crystals and appears also in superconductivity questions in large domains.