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

Abstract

We consider the 3D Pauli operator with nonconstant magnetic field $\mathbf{B}$ 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.