Spectral Asymptotic for the Infinite Mass Dirac Operator in bounded domain

Abstract

In this paper, we study a singular perturbation of a problem used in dimension two to model graphene or in dimension three to describe the quark confinement phenomenon in hadrons. The operators we consider are of the form $H+M\beta V(x)$, where $H$ is the free Dirac operator, $\beta$ is a constant matrix, $V(x)$ is a real valued piecewise constant potential having a jump discontinuity across a smooth interface and $M$ is the mass that we can see as a coupling constant. In particular, we perform a complete asymptotic expansion of spectral quantities as the mass $M$ tends to $+\infty$.