Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States

A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form H=ωJ₃+αJ₋+βJ₊, α≠β, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmet...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2010
Hauptverfasser: Cherbal, O., Drir, M., Maamache, M., Trifonov, D.A.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2010
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146526
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States / O. Cherbal, M. Drir, M. Maamache, D.A. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 33 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146526
record_format dspace
spelling Cherbal, O.
Drir, M.
Maamache, M.
Trifonov, D.A.
2019-02-09T19:59:54Z
2019-02-09T19:59:54Z
2010
Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States / O. Cherbal, M. Drir, M. Maamache, D.A. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 33 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81Q12; 81Q60; 81R30
DOI:10.3842/SIGMA.2010.096
https://nasplib.isofts.kiev.ua/handle/123456789/146526
A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form H=ωJ₃+αJ₋+βJ₊, α≠β, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.
This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
spellingShingle Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
Cherbal, O.
Drir, M.
Maamache, M.
Trifonov, D.A.
title_short Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
title_full Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
title_fullStr Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
title_full_unstemmed Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
title_sort supersymmetric extension of non-hermitian su(2) hamiltonian and supercoherent states
author Cherbal, O.
Drir, M.
Maamache, M.
Trifonov, D.A.
author_facet Cherbal, O.
Drir, M.
Maamache, M.
Trifonov, D.A.
publishDate 2010
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form H=ωJ₃+αJ₋+βJ₊, α≠β, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146526
citation_txt Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States / O. Cherbal, M. Drir, M. Maamache, D.A. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 33 назв. — англ.
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AT trifonovda supersymmetricextensionofnonhermitiansu2hamiltonianandsupercoherentstates
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