Dirac operators on the half-line: stability of spectrum and non-relativistic limit

TL;DR

This paper investigates Dirac operators on the half-line with boundary conditions, establishing spectral stability criteria under perturbations and connecting the non-relativistic limit to Robin Laplacians.

Contribution

It provides new conditions for spectral stability of Dirac operators under potential perturbations and links the non-relativistic limit to Robin Laplacians on the half-line.

Findings

Spectral stability conditions derived for Dirac operators.

Optimality analysis of the stability results.

Non-relativistic limit relates Dirac operators to Robin Laplacians.

Abstract

We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations and study the optimality of the obtained results. Finally, we establish a non-relativistic limit which makes a relationship of the present model to the Robin Laplacian on the half-line.