Birkhoffian Symplectic Scheme for a Quantum System

作     者：苏红玲 

作者机构：Department of MathematicsRenmin University of China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2010年第53卷第3期

页      面：476-480页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Nature Science Foundation of China under Grant No. 10701081 

主　　题：quantum system Birkhoffian symplectic scheme local energy conservation law perturbed Hamiltonian system 

摘      要：In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.