Spectral analysis of the Dirac operator with a singular interaction on a broken line

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00598052" target="_blank" >RIV/61389005:_____/24:00598052 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1063/5.0202693" target="_blank" >https://doi.org/10.1063/5.0202693</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0202693" target="_blank" >10.1063/5.0202693</a>

Result language
angličtina
Original language name
Spectral analysis of the Dirac operator with a singular interaction on a broken line
Original language description
We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar delta-shell interaction of strength tau is an element of R{-2,0,2} supported on a broken line of opening angle 2 omega with omega is an element of(0,pi/2). The essential spectrum of any such self-adjoint realization is symmetric with respect to the origin with a gap around zero whose size depends on the mass and, for tau < 0, also on the strength of the interaction, but does not depend on omega. As the main result, we prove that for any N is an element of N and strength tau is an element of (-infinity, 0){-2} the discrete spectrum of any such self-adjoint realization has at least N discrete eigenvalues, with multiplicities taken into account, in the gap of the essential spectrum provided that omega is sufficiently small. Moreover, we obtain an explicit estimate on omega sufficient for this property to hold. For tau is an element of (0, infinity){2}, the discrete spectrum consists of at most one simple eigenvalue.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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