On Dirac operators in R3 with electrostatic and Lorentz scalar delta-shell interactions
Result description
In this article, Dirac operators A eta,tau coupled with combinations of electrostatic and Lorentz scalar delta -shell interactions of constant strength eta and tau, respectively, supported on compact surfaces Sigma subset of R3 are studied. In the rigorous definition of these operators, the delta -potentials are modeled by coupling conditions at Sigma. In the proof of the self-adjointness of A eta,tau, a Krein-type resolvent formula and a Birman-Schwinger principle are obtained. With their help, a detailed study of the qualitative spectral properties of A eta,tau is possible. In particular, the essential spectrum of A eta,tau is determined, it is shown that at most finitely many discrete eigenvalues can appear, and several symmetry relations in the point spectrum are obtained. Moreover, the nonrelativistic limit of A eta,tau is computed and it is discussed that for some special interaction strengths, A eta,tau is decoupled to two operators acting in the domains with the common boundary Sigma.
Keywords
Dirac operatorShell interactioncoupling conditionSpectral analysisNonrelativistic limit
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On Dirac operators in R3 with electrostatic and Lorentz scalar delta-shell interactions
Original language description
In this article, Dirac operators A eta,tau coupled with combinations of electrostatic and Lorentz scalar delta -shell interactions of constant strength eta and tau, respectively, supported on compact surfaces Sigma subset of R3 are studied. In the rigorous definition of these operators, the delta -potentials are modeled by coupling conditions at Sigma. In the proof of the self-adjointness of A eta,tau, a Krein-type resolvent formula and a Birman-Schwinger principle are obtained. With their help, a detailed study of the qualitative spectral properties of A eta,tau is possible. In particular, the essential spectrum of A eta,tau is determined, it is shown that at most finitely many discrete eigenvalues can appear, and several symmetry relations in the point spectrum are obtained. Moreover, the nonrelativistic limit of A eta,tau is computed and it is discussed that for some special interaction strengths, A eta,tau is decoupled to two operators acting in the domains with the common boundary Sigma.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Quantum Studies: Mathematics and Foundations
ISSN
2196-5609
e-ISSN
2196-5617
Volume of the periodical
6
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
295-314
UT code for WoS article
000612865800003
EID of the result in the Scopus database
2-s2.0-85081344355
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Year of implementation
2019