Resonances for Dirac operators on the half-line

TL;DR

This paper investigates the resonances of one-dimensional Dirac operators on the half-line with compactly supported potentials, analyzing their distribution, asymptotics, and bounds to deepen understanding of their spectral properties.

Contribution

It provides new results on the asymptotic behavior, estimates, and forbidden domains of resonances for 1D Dirac operators with compactly supported potentials.

Findings

Asymptotics of the resonance counting function

Estimates on the location of resonances

Identification of forbidden resonance domains

Abstract

We consider the 1D Dirac operator on the half-line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: 1) asymptotics of counting function, 2) estimates on the resonances and the forbidden domain.