Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory
In this paper we investigate time-dependent non-Hermitian Hamiltonians, which consist of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as ps...
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Elsevier
2022-12-01
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| Series: | Physics Open |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666032622000278 |
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| author | Nadjat Amaouche Maroua Sekhri Rahma Zerimeche Mustapha Maamache J.-Q. Liang |
| author_facet | Nadjat Amaouche Maroua Sekhri Rahma Zerimeche Mustapha Maamache J.-Q. Liang |
| author_sort | Nadjat Amaouche |
| collection | DOAJ |
| description | In this paper we investigate time-dependent non-Hermitian Hamiltonians, which consist of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1) and SU(2) systems in a unified manner. Then, we derive the Lewis–Riesenfeld (LR) phase, which can be separated into the dynamic and the geometrical phases. The analytical results are well consistent with those of the corresponding Hermitian Hamiltonians reported in the literature. |
| first_indexed | 2024-04-11T07:44:53Z |
| format | Article |
| id | doaj.art-2d06ce2da6344327bf351000b53b8979 |
| institution | Directory Open Access Journal |
| issn | 2666-0326 |
| language | English |
| last_indexed | 2024-04-11T07:44:53Z |
| publishDate | 2022-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Open |
| spelling | doaj.art-2d06ce2da6344327bf351000b53b89792022-12-22T04:36:20ZengElsevierPhysics Open2666-03262022-12-0113100126Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theoryNadjat Amaouche0Maroua Sekhri1Rahma Zerimeche2Mustapha Maamache3J.-Q. Liang4Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, AlgeriaLaboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, AlgeriaLaboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, Algeria; Physics Department, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel, AlgeriaLaboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Universite Ferhat Abbas Sétif 1, Sétif 19000, Algeria; Corresponding author.Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, Shanxi 030006, ChinaIn this paper we investigate time-dependent non-Hermitian Hamiltonians, which consist of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1) and SU(2) systems in a unified manner. Then, we derive the Lewis–Riesenfeld (LR) phase, which can be separated into the dynamic and the geometrical phases. The analytical results are well consistent with those of the corresponding Hermitian Hamiltonians reported in the literature.http://www.sciencedirect.com/science/article/pii/S2666032622000278Non-Hermitian HamiltonianSU(1, 1) and SU(2) Lie algebraPseudo-Hermitian invariant |
| spellingShingle | Nadjat Amaouche Maroua Sekhri Rahma Zerimeche Mustapha Maamache J.-Q. Liang Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory Physics Open Non-Hermitian Hamiltonian SU(1, 1) and SU(2) Lie algebra Pseudo-Hermitian invariant |
| title | Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory |
| title_full | Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory |
| title_fullStr | Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory |
| title_full_unstemmed | Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory |
| title_short | Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory |
| title_sort | non hermitian hamiltonian beyond pt symmetry for time dependent su 1 1 and su 2 systems exact solution and geometric phase in pseudo invariant theory |
| topic | Non-Hermitian Hamiltonian SU(1, 1) and SU(2) Lie algebra Pseudo-Hermitian invariant |
| url | http://www.sciencedirect.com/science/article/pii/S2666032622000278 |
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