158,754 research outputs found
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
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