Self-adjointness for the MIT bag model on an unbounded cone

We consider the massless Dirac operator with the MIT bag boundary conditions on an unbounded three-dimensional circular cone. For convex cones, we prove that this operator is self-adjoint defined on four-component $H^1$--functions satisfying the MIT bag boundary conditions. The proof of this result...

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Bibliographic Details
Main Authors Cassano, Biagio, Lotoreichik, Vladimir
Format Journal Article
LanguageEnglish
Published 20.01.2022
Subjects
Mathematics - Analysis of PDEs
Mathematics - Functional Analysis
Mathematics - Mathematical Physics
Mathematics - Spectral Theory
Physics - Mathematical Physics
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Summary:We consider the massless Dirac operator with the MIT bag boundary conditions on an unbounded three-dimensional circular cone. For convex cones, we prove that this operator is self-adjoint defined on four-component $H^1$--functions satisfying the MIT bag boundary conditions. The proof of this result relies on separation of variables and spectral estimates for one-dimensional fiber Dirac-type operators. Furthermore, we provide a numerical evidence for the self-adjointness on the same domain also for non-convex cones. Moreover, we prove a Hardy-type inequality for such a Dirac operator on convex cones, which, in particular, yields stability of self-adjointness under perturbations by a class of unbounded potentials. Further extensions of our results to Dirac operators with quantum dot boundary conditions are also discussed.
DOI:10.48550/arxiv.2201.08192