General δ-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
Result description
In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator. In the non-critical case, we do so by providing a boundary triple, and in the critical purely magnetic case, by exploiting the phenomenon of confinement and super-symmetry. Moreover, we justify our model by showing that Dirac operators with singular interactions are limits in the strong resolvent sense of Dirac operators with regular potentials.
Keywords
Dirac operatorquantum-dotLorentz-scalar 8-shellboundary conditionsself-adjoint operatorconformal map
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/23:00369759
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
General δ-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
Original language description
In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator. In the non-critical case, we do so by providing a boundary triple, and in the critical purely magnetic case, by exploiting the phenomenon of confinement and super-symmetry. Moreover, we justify our model by showing that Dirac operators with singular interactions are limits in the strong resolvent sense of Dirac operators with regular potentials.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista Matematica Iberoamericana
ISSN
0213-2230
e-ISSN
—
Volume of the periodical
39
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
50
Pages from-to
1443-1492
UT code for WoS article
001044706500010
EID of the result in the Scopus database
2-s2.0-85166117067
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2023