Time Evolution of a Two-Dimensional Classical Lattice System

Abstract

We exhibit a dynamical model of particles in a two-dimensional lattice. We study a particular class of equilibrium states, and we investigate the simplest time correlation functions for these states. As a consequence, the propagation of sound waves with velocity $\frac{1}{\sqrt{2}}$ can be proved rigorously. A transport coefficient analogous to a viscosity is given by a Kubo-type integral formula. The convergence of the integral is discussed. Some preliminary computer results are reported.