Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 069, 17 pages      arXiv:0707.2736      https://doi.org/10.3842/SIGMA.2009.069
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''

Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution

Alexander I. Nesterov
Departamento de Física, CUCEI, Universidad de Guadalajara, Av. Revolución 1500, Guadalajara, CP 44420, Jalisco, México

Received November 17, 2008, in final form June 23, 2009; Published online July 07, 2009

Abstract
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.

Key words: non-Hermitian quantum systems; quantum brachistochrone problem.

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