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Two-dimensional Dirac operators with singular interactions supported on closed curves

Behrndt, Jussi; Holzmann, Markus; Ourmières-Bonafos, Thomas; Pankrashkin, Konstantin (2019-07), Two-dimensional Dirac operators with singular interactions supported on closed curves. https://basepub.dauphine.fr/handle/123456789/20149

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02181432
Date
2019-07
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
52
Metadata
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Author(s)
Behrndt, Jussi

Holzmann, Markus

Ourmières-Bonafos, Thomas
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Pankrashkin, Konstantin
Laboratoire de Mathématiques d'Orsay [LMO]
Abstract (EN)
This paper is devoted to the study of the two-dimensional Dirac operator with an arbitrary combination of an electrostatic and a Lorentz scalar δ-interaction of constant strengths supported on a closed curve. For any combination of the coupling constants a rigorous description of the self-adjoint realization of the operators is given and the spectral properties are described. For a non-zero mass and a critical combination of coupling constants the operator appears to have an additional point in the essential spectrum, which is related to a loss of regularity in the operator domain, and the position of this point is expressed in terms of the coupling constants.
Subjects / Keywords
Two-dimensional Dirac operators; closed curves