Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution

作者：Nesterov Alexander I^*

来源：Symmetry Integrability and Geometry-Methods and Applications, 2009, 5: 069.

DOI：10.3842/SIGMA.2009.069

• non-Hermitian quantum systems
• quantum brachistochrone problem

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 vertical bar psi(i)> into a specific final state vertical bar psi(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 vertical bar psi(i)> and vertical bar psi(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.

• 出版日期2009