Normal transport properties for a classical particle coupled to a non-Ohmic bath

Abstract

We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a stationary state, because the oscillators cannot effectively absorb the energy of high speed particles. We nonetheless show that the system has at all positive temperatures a well-defined low-field mobility over macroscopic time scales of order exp(-c/F). The mobility is independent of F at low fields, and related to the zero-field diffusion constant D through the Einstein relation. The system therefore exhibits normal transport even though the bath obviously has a discrete frequency spectrum (it is simply monochromatic) and is therefore highly non-Ohmic. Such features are usually associated with anomalous transport properties.