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Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
Інший ID:
2000 Mathematics Subject Classification: 81S10; 81V99; 53Z05
Посилання:
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.
Підтримка:
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.
Дата:
2009
Переглядів:
332
Завантажень:
204
Анотація:
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.
