Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian PT-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state |ψi> into a specific final state |ψf> can be made arbitrarily small. Addition...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149118 |
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| Zitieren: | Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution / A.I. Nesterov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 42 назв. — англ. |
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Nesterov, A.I. 2019-02-19T17:30:24Z 2019-02-19T17:30:24Z 2009 Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution / A.I. Nesterov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 42 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81S10; 81V99; 53Z05 https://nasplib.isofts.kiev.ua/handle/123456789/149118 Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian PT-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state |ψi> into a specific final state |ψf> can be made arbitrarily small. Additionally, it has been shown that finding the shortest possible time requires only the solution of the two-dimensional problem for the quantum system governed by the effective Hamiltonian acting in the subspace spanned by |ψi> and |ψf>. In this paper, we study a similar problem for the generic non-Hermitian Hamiltonian, focusing our attention on the geometric aspects of the problem. This paper is a contribution to the Proceedings of the VIIth Workshop “Quantum Physics with NonHermitian Operators” (June 29 – July 11, 2008, Benasque, Spain). The author is grateful to C. Bender, D. Brody, U. G¨unther, A. Mostafazadeh, I. Rotter and B.F. Samsonov for helpful discussions and comments. This work is supported by research grants SEP-PROMEP 103.5/04/1911. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution |
| spellingShingle |
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution Nesterov, A.I. |
| title_short |
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution |
| title_full |
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution |
| title_fullStr |
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution |
| title_full_unstemmed |
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution |
| title_sort |
non-hermitian quantum systems and time-optimal quantum evolution |
| author |
Nesterov, A.I. |
| author_facet |
Nesterov, A.I. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian PT-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state |ψi> into a specific final state |ψf> can be made arbitrarily small. Additionally, it has been shown that finding the shortest possible time requires only the solution of the two-dimensional problem for the quantum system governed by the effective Hamiltonian acting in the subspace spanned by |ψi> and |ψf>. In this paper, we study a similar problem for the generic non-Hermitian Hamiltonian, focusing our attention on the geometric aspects of the problem.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149118 |
| citation_txt |
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution / A.I. Nesterov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 42 назв. — англ. |
| work_keys_str_mv |
AT nesterovai nonhermitianquantumsystemsandtimeoptimalquantumevolution |
| first_indexed |
2025-11-29T05:17:59Z |
| last_indexed |
2025-11-29T05:17:59Z |
| _version_ |
1850854546286313472 |