Computer Studies on the Approach to Thermal Equilibrium in Coupled Anharmonic Oscillators. I. Two Dimensional Case

Abstract

The long-time behaviors of the vibration in two dimensional square lattice with central and noncentral forces between nearest neighbors are calculated on computer. The forces are assumed to have quartic potentials with the anharmonic coupling constant λ besides the harmonic ones. Computer experiments revealed the existence of the induction period, and after the elapse of the induction period, the energy sharing takes place among various modes and the system tends to reach a thermal equilibrium. The induction period becomes large for small coupling constant λ and seems to become infinity at a small critical value of λ₀. When λ is less than this critical value λ₀, the system is almost periodic, but when λ is larger than λ₀, the system becomes ergodic.