The spectral density of the scattering matrix of the magnetic Schrodinger operator for high energies

TL;DR

This paper derives an explicit formula for the asymptotic eigenvalue density of the scattering matrix associated with the magnetic Schrödinger operator at high energies, depending solely on the magnetic vector potential.

Contribution

It provides a new explicit formula for the eigenvalue density of the scattering matrix in the high energy limit, focusing on magnetic potentials.

Findings

Explicit formula for eigenvalue density involving magnetic vector potential

Asymptotic behavior characterized at high energies

Results applicable to smooth short-range potentials

Abstract

The scattering matrix of the Schrodinger operator with smooth short-range electric and magnetic potentials is considered. The asymptotic density of the eigenvalues of this scattering matrix in the high energy regime is determined. An explicit formula for this density is given. This formula involves only the magnetic vector-potential.