P. Lafitte, P. E. Parris, S. De Bievre
Normal transport properties for a classical particle coupled to a non-Ohmic bath
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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 \emph{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 $\mu $ 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.