RESEARCH ON ERGODIC PROBLEMS IN HAMILTONIAN DYNAMICS

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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.