Lowest energy band function for magnetic steps

TL;DR

This paper analyzes the spectral properties of a Schrödinger operator with a step magnetic field, establishing the unique minimum of its lowest eigenvalue band and exploring how curvature influences magnetic ground state localization.

Contribution

It proves the existence and uniqueness of a non-degenerate minimum of the lowest eigenvalue band function for the Schrödinger operator with step magnetic field.

Findings

Unique non-degenerate minimum of the eigenvalue band function established

Curvature effects on magnetic ground state localization discussed

Spectral properties characterized for the step magnetic field case

Abstract

We study the Schr\"odinger operator in the plane with a step magnetic field function. The bottom of its spectrum is described by the infimum of the lowest eigenvalue band function, for which we establish the existence and uniqueness of the non-degenerate minimum. We discuss the curvature effects on the localization properties of magnetic ground states, among other applications.