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Self-adjointness for the MIT bag model on an unbounded cone
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SYSNO ASEP 0581041 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Self-adjointness for the MIT bag model on an unbounded cone Author(s) Cassano, B. (IT)
Lotoreichik, Vladimir (UJF-V) ORCID, SAINumber of authors 2 Source Title Mathematische Nachrichten - ISSN 0025-584X
Roč. 297, č. 3 (2024), s. 1006-1041Number of pages 36 s. Publication form Print - P Language eng - English Country DE - Germany Keywords Dirac operator ; Hardy inequality ; MIT bag model ; ortogonal decomposition ; self-adjointness ; unbounded circular cone OECD category Pure mathematics R&D Projects GA21-07129S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support UJF-V - RVO:61389005 UT WOS 001119385200001 EID SCOPUS 85173902293 DOI 10.1002/mana.202200386 Annotation 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 H1-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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2025 Electronic address https://doi.org/10.1002/mana.202200386
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