Symmetry, Integrability and Geometry: Methods and Applications (Jul 2009)
Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
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 |ψ_i> into a specific final state |ψ_f> 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 |ψ_i> and |ψ_f>. In this paper, we study a similar problem for the generic non-Hermitian Hamiltonian, focusing our attention on the geometric aspects of the problem.
