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

2009/08/25 by Georgi Raikov, Georgi D. Raikov, Raikov, Georgi D.
Computer Science · Mathematics · #35J10 #35P20 #35P25 #47F05 #81Q10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.AP #math.SP #msc:35J10 #msc:35P20 #msc:35P25 #msc:47F05 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.0908.3704

24 pages, to appear in Publ. Res. Inst. Math. Sci., typos corrected

openalex publication_date 2009/08/25 · arxiv created 2010/06/29 · arxiv updated 2010/06/30 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

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.

Related

• Asymptotics near +-m of the spectral shift function for Dirac operators with non-constant magnetic fields
• Spectral Asymptotics for Magnetic Schroedinger Operator
• A simple criterion for the existence of nonreal eigenvalues for a class\n of 2D and 3D Pauli operators
• Weak coupling asymptotics for the Pauli operator in two dimensions
• Counting function of magnetic eigenvalues for non-definite sign perturbations