Spectral Transition for Dirac Operators with Electrostatic [Formula: see text] -Shell Potentials Supported on the Straight Line

Jussi Behrndt; Markus Holzmann; Matěj Tušek

doi:10.1007/s00020-022-02711-6

Spectral Transition for Dirac Operators with Electrostatic $δ$ -Shell Potentials Supported on the Straight Line

Integr Equ Oper Theory. 2022;94(3):33. doi: 10.1007/s00020-022-02711-6. Epub 2022 Aug 30.

Authors

Jussi Behrndt¹, Markus Holzmann¹, Matěj Tušek²

Affiliations

¹ Institut für Angewandte Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.
² Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic.

Abstract

In this note the two dimensional Dirac operator $A_{η}$ with an electrostatic $δ$ -shell interaction of strength $η \in R$ supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths $η = \pm 2$ the continuous spectrum of $A_{η}$ inside the spectral gap of the free Dirac operator $A_{0}$ collapses abruptly to a single point.

Keywords: Boundary triple; Dirac operator; Singular potential; Spectral transition.

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