title: On van der Waals friction between half-spaces at low temperature.
abstract: We determine, in the van der Waals regime (neglecting retardation and relativistic effects), the frictional power loss P and the drag force F = P/u per unit area between two Drude-modelled half-spaces, with surface plasmon frequency ω(S) and realistically weak dissipation, separated by a gap of width ζ, and constrained to uniform parallel motion with relative speed u. The calculation uses only textbook-level adiabatic and perturbative methods of nonrelativistic quantum mechanics. The initial temperature is taken to be low, with τ ≡ k(B)T/ħω(S) << 1. At strictly zero temperature, P is proportional to u(4)/ζ(6) when ν ≡ u/ω(S)ζ << 1, and to 1/uζ when ν >> 1. But at fixed nonzero τ, as v rises from zero, P is at first dominated by a temperature-dependent component proportional to u(2)T(2)/ζ(4). The assumptions of the model as regards the half-spaces are satisfied by most quantum-electrodynamics-based approaches, whose results in the nonretarded limit should therefore be the same as ours. We also find that the frequency distribution of the friction-induced energy increments is not thermal, suggesting that in this respect the Huttner-Barnett theory (which we use to describe dissipative materials) needs further refinement.
authors.affiliation: Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK. g.barton@sussex.ac.uk
authors.forename: Gabriel
authors.initials: G
authors.lastname: Barton