On the essential spectrum of two-dimensional Pauli operators with repulsive potentials

TL;DR

This paper analyzes the spectrum of a two-dimensional Pauli operator with a magnetic field and a growing negative potential, providing criteria for the presence of discrete and dense spectra.

Contribution

It offers new criteria to determine when the Pauli operator's spectrum is discrete or dense, considering potentials that grow at infinity.

Findings

Criteria for discrete spectrum established

Conditions for dense spectrum identified

Insights into spectral behavior with growing potentials

Abstract

We investigate the spectrum of the two-dimensional Pauli operator, describing a spin-$1/2$ particle in a magnetic field $B$, with a negative scalar potential $V$ such that $|V|$ grows at infinity. In particular, we obtain criteria for discrete and dense pure-point spectrum.