A linear chain of atoms, interacting with anharmonic forces, one of whose end atoms is forced to vibrate harmonically, is studied as a simple model for kinetic friction between ideal crystalline solids. It is found that there is a transition, as a function of chain length and driving frequency between a regime in which there is dissipation (i.e., the internal energy increases as a function of time on the average) and one in which there is practically no dissipation. This suggests that there can be dissipationless sliding fro sufficiently small solids.
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J. B. Sokoloff (1993) studied this question.