RESEARCH ON ERGODIC PROBLEMS IN HAMILTONIAN DYNAMICS

1. 从滞流层中浸没的结垢结构解释了长时间尾的起源。我们提出了静止层理论来描述哈密顿动力学的非平稳性和多遍历性。关于散射过程和晶格振动的计算机模拟证实了理论结果。从量子混沌的角度描述了波函数和能级的不规则性。Gutzwiller公式是从有限元法的半经典近似中重新推导出来的。从分布函数的弱收敛性出发，讨论了不可逆性的量子和经典起源。量子系统中的不可逆性被特别推测为发生在极限[j]。[)->0用于Hushimi函数。

1. The origin of the long time tail was explained from the scaling structures immersed in the stagnant layr. We have propsed the stagnant layr theory to characterize the non-stationrity and the multi-ergodicity of Hamiltonian dynamics. Computer simulations regarding scattering processes and lattice vibrations have justified the theoretical results.2. The irregulatiry of wave functions and energy levels was characterized from the viewpoint of quantum chaos. The Gutzwiller formulae was rederived from the semi-classical approximation of the finite element method.3. The origin of the irreversibility, both in quantal and in classical, was discussed from the weak convergence of the distribution function. The irreversibility in quantal systems was especially surmised to occur in the limit (〕SY.plcnst.〔)->0 for Hushimi functions.