KINETIC-ISING-MODEL DESCRIPTION OF NEWTONIAN DYNAMICS - A ONE-DIMENSIONAL EXAMPLE

We show that the Newtonian dynamics of a chain of particles with an an harmonic on-site potential and harmonic nearest-neighbor interactions can be described by a one-dimensional kinetic Ising model with most ge neral Glauber transition rates, provided the temperature is low enough compared to the minimum barrier height. The transition rates are calc ulated by use of the transition-state theory. At higher temperatures, memory effects occur which invalidate this kinetic description. These memory effects are due to the appearance of dynamically correlated clu sters of particles performing periodic oscillations over a certain tim e scale.