2019/09/09 by Badreddine Benhellal, Benhellal, Badreddine
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Graphene research and applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1909.03769
openalex publication_date 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 + MβV (x), where H is the free Dirac operator, β 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 +∞.