Low Energy Asymptotics of the Spectral Shift Function for Pauli Operators with Nonconstant Magnetic Fields

TL;DR

This paper studies the low-energy behavior of the spectral shift function for 3D Pauli operators with nonconstant magnetic fields and electric potentials, deriving a generalized Levinson formula for negative potentials.

Contribution

It provides new asymptotic results for the spectral shift function and establishes a generalized Levinson formula in this setting.

Findings

Derived low-energy asymptotics of the spectral shift function.

Established a generalized Levinson formula for negative potentials.

Linked eigenvalue counting and scattering phase asymptotics.

Abstract

We consider the 3D Pauli operator with nonconstant magnetic field B of constant direction, perturbed by a symmetric matrix-valued electric potential V whose coefficients decay fast enough at infinity. We investigate the low-energy asymptotics of the corresponding spectral shift function. As a corollary, for generic negative V, we obtain a generalized Levinson formula, relating the low-energy asymptotics of the eigenvalue counting function and of the scattering phase of the perturbed operator.