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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| Дата: | 2010 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146526 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1465262019-02-10T01:25:21Z Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States Cherbal, O. Drir, M. Maamache, M. Trifonov, D.A. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146526 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cherbal, O. Drir, M. Maamache, M. Trifonov, D.A. |
| spellingShingle |
Cherbal, O. Drir, M. Maamache, M. Trifonov, D.A. Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cherbal, O. Drir, M. Maamache, M. Trifonov, D.A. |
| author_sort |
Cherbal, O. |
| title |
Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:00Z |
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