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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2009 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2009
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149118 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862613101370671104 |
|---|---|
| author | Nesterov, A.I. |
| author_facet | Nesterov, A.I. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-11-29T05:17:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149118 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-29T05:17:59Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution Nesterov, A.I. |
| title | 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_short | Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution |
| title_sort | non-hermitian quantum systems and time-optimal quantum evolution |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149118 |
| work_keys_str_mv | AT nesterovai nonhermitianquantumsystemsandtimeoptimalquantumevolution |