Eigenvalue Curves for Generalized MIT Bag Models

Autor: Naiara Arrizabalaga, Albert Mas, Tomás Sanz-Perela, Luis Vega
Přispěvatelé: Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. TP-EDP - Grup de Teoria de Funcions i Equacions en Derivades Parcials
Rok vydání: 2022
Předmět:
Zdroj: Communications in Mathematical Physics. 397:337-392
ISSN: 1432-0916
0010-3616
Popis: We study spectral properties of Dirac operators on bounded domains $\Omega \subset \mathbb{R}^3$ with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter $\tau\in\mathbb{R}$; the case $\tau = 0$ corresponds to the MIT bag model. We show that the eigenvalues are parametrized as increasing functions of $\tau$, and we exploit this monotonicity to study the limits as $\tau \to \pm \infty$. We prove that if $\Omega$ is not a ball then the first positive eigenvalue is greater than the one of a ball with the same volume for all $\tau$ large enough. Moreover, we show that the first positive eigenvalue converges to the mass of the particle as $\tau \downarrow -\infty$, and we also analyze its first order asymptotics.
Comment: 49 pages, 5 figures. v2: version after referee report (Conjecture 1.8 and Remark 1.9 added) v3: Final version
Databáze: OpenAIRE
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