COMPUTER STUDIES ON APPROACH TO THERMAL EQUILIBRIUM IN COUPLED ANHARMONIC OSCILLATORS .2. ONE-DIMENSIONAL CASE

One-dimensional anharmonic lattices with quadratic as well as quartic potentials between nearest neighbors are treated on computer to see the longtime behaviors of the vibration. As is the case of two-dimensional lattice, the induction period is found to exist and its length increases on decreasing the anharmonic coupling constant. The possible existence of the critical value of the anharmonic coupling constant is surmised, below which the system is almost periodic. Above this critical value, the system tends to reach a thermal equilibrium, which is confirmed by the long-time averages of the squares of the velocities and by the products of velocities of different particles. The significance of the errors introduced during computation for the ergodic property of the system is pointed out. © 1969, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.