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

Jussi Behrndt; Markus Holzmann; Matej Tusek

doi:10.1007/s00020-022-02711-6

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

Institute of Applied Mathematics (5040)

Research output: Contribution to journal › Article › peer-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 language	English
Article number	33
Journal	Integral Equations and Operator Theory
Volume	94
Issue number	3
DOIs	https://doi.org/10.1007/s00020-022-02711-6
Publication status	Published - Sep 2022

Keywords

Boundary triple
Dirac operator
Singular potential
Spectral transition

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-022-02711-6Licence: CC BY 4.0

Cite this

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

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.",

keywords = "Boundary triple, Dirac operator, Singular potential, Spectral transition",

author = "Jussi Behrndt and Markus Holzmann and Matej Tusek",

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doi = "10.1007/s00020-022-02711-6",

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T1 - Spectral Transition for Dirac Operators with Electrostatic δ -Shell Potentials Supported on the Straight Line

AU - Behrndt, Jussi

AU - Holzmann, Markus

AU - Tusek, Matej

PY - 2022/9

Y1 - 2022/9

N2 - 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.

AB - 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.

KW - Boundary triple

KW - Dirac operator

KW - Singular potential

KW - Spectral transition

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U2 - 10.1007/s00020-022-02711-6

DO - 10.1007/s00020-022-02711-6

M3 - Article

VL - 94

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

M1 - 33

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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