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
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02181432
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / KeywordsTwo-dimensional Dirac operators; closed curves
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