Pseudomodes for non-self-adjoint Dirac operators

TL;DR

This paper develops a systematic non-semi-classical method to construct pseudomodes for one-dimensional Dirac operators with complex potentials, advancing understanding of their spectral properties and covering a broad class of potentials.

Contribution

It introduces a novel non-semi-classical approach to construct pseudomodes for Dirac operators, enabling analysis of more general and complex potentials.

Findings

Constructed pseudomodes for large pseudoeigenvalues

Achieved optimal conditions for a wide class of potentials

Extended analysis to superexponential potentials

Abstract

Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic non-semi-classical approach, which results in substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including superexponential ones.