Dirac bag model on thin domains: a microlocal viewpoint

TL;DR

This paper investigates the spectral properties of the Dirac operator on thin two-dimensional domains with infinite mass boundary conditions, using microlocal analysis to provide new insights into its discrete spectrum and asymptotic behavior.

Contribution

It offers a novel microlocal analysis perspective on the Dirac operator's spectrum in thin domains, revisiting and extending recent results.

Findings

Discrete spectrum existence established

Asymptotic behavior characterized in thin limit

Microlocal analysis provides new insights

Abstract

The Dirac operator is considered on a bidimensional domain whose boundary carries the infinite mass boundary condition. The analysis is focused on the existence of discrete spectrum and on its asymptotic description in the thin width limit. We revisit a recent result by using an alternative view point inspired by microlocal analysis.