二维形变谐振子系统中的量子经典对应

Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System

通过引入等效普朗克常数 ,将量子系统中基本动力学变量的期望值和经典系统中基本动力学变量的精确值的时间演化行为相比较 ,分析了两者产生差异的因素 ,规则运动主要是和量子效应有关 ,而混沌运动则是和动力学效应有关 ,即与系统的动力学对称性破坏相联系 .在此基础上 ,比较了量子相空间测不准度和李雅谱诺夫指数 。

The time evolution of expectation values of the basic dynamic variables in a quantum system under different effective Planck constant were compared with the exact values of the basic dynamic variables in classical system. It is found, for the regular motion, the difference comes from the quantum effect; for the chaotic motion, it comes from the dynamical effect and the destruction of the dynamical system. With these results, a correspondence between the quantum heterogeneity of the phase space and the Lyapunov exponent is made satisfactorily.