Ohmic Response of a Classical Particle Coupled to a non-Ohmic Bath

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 has, over macroscopic time scales, both a well-defined low-field mobility μ that is independent of F , and a well-defined diffusion constant D at zero field. The system therefore exhibits Ohmic behavior in spite of the fact that the bath is strongly non-Ohmic, since its frequency distribution has both an ultraviolet cutoff and an infrared gap. The latter is usually associated with superdiffusive behavior.