Classical analogue of quantum friction

We study the classical analogue of the quantum friction force resulting from interaction of electromagnetic surface states in a pair of monoatomic layers (e.g., graphene sheets) sliding one with respect to another with a nonrelativistic velocity v ≪ c. The layers are modeled as two-dimensional arrays of dipolar oscillators. Using a Hamiltonian formalism we demonstrate that the effect of quantum friction can be explained quasi-classically by a process of parametric amplification of surface waves in such arrays.