Computer Experiments on Ergodic Problems in Anharmonic Lattice Vibrations

Abstract

Various computer experiments based on the numerical integration of dynamical equation of motion are their importance is emphasized in connection with ergodic theory. To do this a short review of the present status of the ergodic theories is also given and the interrelations among various results of ergodic theories are clarified. The inducition period discovered in the previous papers (H. Hirooka and N. Saitô, J. Phys. Soc. Japan 26 (1969), 624; N. Ooyama, H. Hirooka and N. Saitô, J. Phys. Soc. Japan 27 (1969), 815) is further examined in one-dimensional anharmonic lattices including exponential lattices. The apparent randomness which the system exhibits after elapsing the induction period is, strictly speaking, quasi-stochastic in the sence that the process is described completely as deterministic. The “true” stochasticity which seems required in the thermodynamical state will be realized in the thermodynamical limit.