Stochastic dynamics with a mesoscopic bath.

We consider the effects of bath size on the nature of the dynamics and transport properties for two simple models in which the bath is composed of a collinear chain of harmonic oscillators. The first model consists of an untwisted rotating chain (elastic rotor) for which we obtain a non-Markovian equation analogous to the generalized Langevin equation for the rotational degrees of freedom. We demonstrate that the corresponding memory function oscillates with a frequency close to that of the lowest mode of the chain. The second model considered consists of a tagged oscillator in a finite harmonic chain. For this model, we find an additional harmonic force in the generalized Langevin equation for the terminal atom that does not appear in the equation of motion for the semi-infinite chain. It is demonstrated that the force constant for the additional harmonic force scales as 1/N, where N is the number of oscillators in the chain. Using an exact representation for the velocity correlation function, the transport properties of the model are discussed.