Birkhoffian Symplectic Scheme for a Quantum System

作者：Su Hong Ling^*

来源：Communications in Theoretical Physics, 2010, 53(3): 476-480.

DOI：10.1088/0253-6102/53/3/14

• quantum system
• Birkhoffian symplectic scheme
• local energy conservation law
• perturbed Hamiltonian system

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 examples how 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.

• 出版日期2010-3
• 单位中国人民大学