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

Jussi Behrndt, Markus Holzmann*, Matej Tusek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish
Article number33
JournalIntegral Equations and Operator Theory
Volume94
Issue number3
DOIs
Publication statusPublished - Sept 2022

Keywords

  • Boundary triple
  • Dirac operator
  • Singular potential
  • Spectral transition

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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