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

Behrndt, Jussi; Holzmann, Markus; Ourmières-Bonafos, Thomas; Pankrashkin, Konstantin (2020), Two-dimensional Dirac operators with singular interactions supported on closed curves, Journal of Functional Analysis, 279, 8, p. 52. 10.1016/j.jfa.2020.108700

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Journal of Functional Analysis
Volume
279
Number
8
Publisher
Elsevier
Published in
Paris
Pages
52
Publication identifier
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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; Dirac operator with singular interaction; Self-adjoint extension; Boundary triple; Periodic pseudodifferential operators