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 |
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| Datum: | 2010 |
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| Sprache: | English |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146526 |
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| 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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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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2025-12-07T18:10:05Z |
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2025-12-07T18:10:05Z |
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