Resonances for 1D massless Dirac operators

TL;DR

This paper investigates the resonances of 1D massless Dirac operators with compactly supported potentials, providing asymptotic, estimate, and trace formula results related to these resonances.

Contribution

It introduces new asymptotic formulas, estimates, and a trace formula for resonances of 1D massless Dirac operators, advancing understanding of their spectral properties.

Findings

Asymptotics of resonance counting function

Resonance estimates and forbidden domain characterization

Trace formula relating resonances to operator properties

Abstract

We consider the 1D massless Dirac operator on the real 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, 3) the trace formula in terms of resonances.