Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies

TL;DR

This paper proves a limiting absorption principle for certain long-range perturbations of Dirac systems at threshold energies, using a novel positive commutator approach for non-self-adjoint operators, with applications to quantum dispersive models.

Contribution

It introduces a new positive commutator method for non-self-adjoint operators and applies it to Dirac systems with long-range interactions at threshold energies.

Findings

Established limiting absorption principle for Dirac systems with long-range perturbations.

Developed a positive commutator theory for non-self-adjoint operators.

Applied results to quantum dispersive Helmholtz models.

Abstract

We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to study a family of non-self-adjoint operators. The technique is based on a positive commutator theory for non self-adjoint operators, which we develop in appendix. We also discuss some applications to the dispersive Helmholzt model in the quantum regime.