Irreversibility and Interatomic Potentials in One-dimensional Lattice Models

Abstract

Since the computational work on the relaxation process toward the equilibrium state by Fermi, Pasta, and Ulam (FPU) 1], the stochastic behaviors in one dimensional lattice models have been studied by many physicists numerically and theoretically. The objective of those studies is to understand the origin of thermodynamical properties from the microscopic particle motions which are determined by the deterministic equations of motion. In the FPU work, since the given energy was too small and anharmonicity was too weak, thermodynamic irreversibility phenomena, which lead to the equipartition of energy among modes, were not observed. Many studies after this work confirmed the existence of the threshold for the chaotic motions 2] 3]. However, the relation of the chaotic motion in the system with many degrees of freedom to the thermodynamical properties is not well understood 4]. The steady lattice thermal conduction in one dimensional lattice poses an interesting problem in this; respect. A clear linear internal temperature gradient was not observed in the FPU model 5], while it was observed in the the ding-a-ling model by Casati et al. 6] and the diatomic Toda lattice (DTL) by Mokross and Büttner 7]. Recently, the system size dependence of the coefficient of thermal conductivity has been studied 8]9] and the Fourier's law of heat conduction is begining to be confirmed in the DTL.