Anomalous Pauli electron states for magnetic fields with tails

TL;DR

This paper investigates the spectral properties of a two-dimensional electron with an anomalous magnetic moment in magnetic fields with specific decay, revealing conditions for the existence of bound states depending on flux and coupling strength.

Contribution

It extends previous spectral results to magnetic fields with slower decay and establishes the existence of bound states in zero flux scenarios under mild conditions.

Findings

At least N+1 bound states when flux exceeds N

Existence of weakly coupled bound states in zero flux case

Bound states depend on flux magnitude and field decay rate

Abstract

We consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli operator are extended to fields with the O(r^{-2-\delta}) decay at infinity: we show that if |F| exceeds an integer N, there is at least N+1 bound states. Furthermore, we prove that weakly coupled bound states exist under mild regularity assumptions also in the zero flux case.