Applications of the potential algebras of the two-dimensional Dirac-like operators
Result description
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2 x 2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of the Hamiltonian that close, centrally extended so(3), so(2, 1) or oscillator algebra. The algebraic framework is used in construction of physically interesting solvable models described by the (2 + 1) dimensional Dirac equation. It is applied in description of open-cage fullerenes where the energies and wave functions of low-energy charge-carriers are computed. The potential algebras are also used in construction of shape-invariant, one-dimensional Dirac operators. We show that shape-invariance of the first-order operators is associated with the N = 4 nonlinear supersymmetry which is represented by both local and nonlocal supercharges. The relation to the shape-invariant non-relativistic systems is discussed as well.
Keywords
potential algebraDirac eyuationsupersymmetryshape-invariance
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
Applications of the potential algebras of the two-dimensional Dirac-like operators
Original language description
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2 x 2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of the Hamiltonian that close, centrally extended so(3), so(2, 1) or oscillator algebra. The algebraic framework is used in construction of physically interesting solvable models described by the (2 + 1) dimensional Dirac equation. It is applied in description of open-cage fullerenes where the energies and wave functions of low-energy charge-carriers are computed. The potential algebras are also used in construction of shape-invariant, one-dimensional Dirac operators. We show that shape-invariance of the first-order operators is associated with the N = 4 nonlinear supersymmetry which is represented by both local and nonlocal supercharges. The relation to the shape-invariant non-relativistic systems is discussed as well.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
GPP203/11/P038: Hidden nonlinear symmetries and supersymmetry in quantum systems
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Physics
ISSN
0003-4916
e-ISSN
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Volume of the periodical
331
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
216-235
UT code for WoS article
000316089700013
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2013