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

A new constant-pressure molecular dynamics method for finite system

In this letter, by writing the volume as a function of coordinates of atoms, we present a new constant-pressure molecular dynamics method with parameters free. This method is specially appropriate for the finite system in which the periodic boundary condition does not exist. Simulations on the carbon nanotube and the Ni nanoparticle clearly demonstrate the validity of the method. By using this method, one can easily obtain the equation of states for the finite system under the external pressure.Comment: RevTex, 5 pages, 3 figures, submitted to Phys. Rev. Let

Mosaic spin models with topological order

We study a class of two-dimensional spin models with the Kitaev-type couplings in mosaic structure lattices to implement topological orders. We show that they are exactly solvable by reducing them to some free Majorana fermion models with gauge symmetries. The typical case with a 4-8-8 close packing is investigated in detail to display the quantum phases with Abelian and non-Abelian anyons. Its topological properties characterized by Chern numbers are revealed through the edge modes of its spectrum.Comment: 4 pages, 3 figures. Final version to appear in Phys. Rev. B as a Rapid Communicatio