High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.Comment: ITP.SB-93-22,17 page

Inconsistences in Interacting Agegraphic Dark Energy Models

It is found that the origin agegraphic dark energy tracks the matter in the matter-dominated epoch and then the subsequent dark-energy-dominated epoch becomes impossible. It is argued that the difficulty can be removed when the interaction between the agegraphic dark energy and dark matter is considered. In the note, by discussing three different interacting models, we find that the difficulty still stands even in the interacting models. Furthermore, we find that in the interacting models, there exists the other serious inconsistence that the existence of the radiation/matter-dominated epoch contradicts the ability of agegraphic dark energy in driving the accelerated expansion. The contradiction can be avoided in one of the three models if some constraints on the parameters hold.Comment: 12 pages, no figure; analysis is added; conclusion is unchange