Friction force with non-instantaneous interaction between moving harmonic oscillators

Abstract

The friction force acting between two weakly interacting, harmonic oscillators which move slowly with respect to each other, is considered. In a previous paper the case of instantaneous interaction was treated (J.S. H∅ye and I. Brevik, Physica A 181 (1992) 413) and the expression for the force was obtained by use of a variety of methods in statistical mechanics. The present paper deals with the case of non-instantaneous interaction. It turns out that in order to obtain a complete description one has to take into account the medium (e.g., a thermal vacuum field or crystal lattice) through which the interaction propagates. We consider successively the cases where one, respectively two, oscillators are present in interaction with the medium. Our discussion has a bearing on the self-interaction problem in classical electrodynamics. As a check of the general formalism, the self-interaction on a dielectric spherical particle moving in a thermal radiation field is evaluated by considering the momentum transfer from absorbed radiation.