Underresolved simulations of heat baths

Some recent numerical and theoretical studies indicate that it .is possible to accurately simulate the macroscopic motion of a particle in a heat bath , comprising coupled oscillators, without accurately resolving the fast fre quencies in the heat bath itself. Here we study this issue further by perfo rming numerical experiments on a wide variety of mechanical heat bath model s, all generalizations of the Ford-Kac oscillator model. The results indica te that the nature of the particle-bath damping in the macroscopic limit cr ucially affects the ability of underresolved simulations to correctly predi ct macroscopic behaviour. In particular, problems for which the damping is local in time pose more severe problems for approximation. The root cause i s that local damping typically arises from the degeneration of a memory ker nel to a delta singularity in the macroscopic limit. The approximation of s uch singularities is a more delicate issue than the approximation of smooth er memory kernels. (C) 2001 Academic Press.