Velocity dependence of the quantum friction force on an atom near a dielectric surface

Different approaches to the problem of the "quantum friction" force F acting on an atom moving with velocity v<<c parallel to a dielectric surface have resulted in different predictions for the way in which F depends on v. For instance, Scheel and Buhmann [Phys. Rev. A 80, 042902 (2009)] and Barton [New J. Phys. 12, 113045 (2010)] and others find a force linear in v, while Intravaia, Behunin, and Dalvit [arXiv:1308.0712, 2013] and others find that the force varies as v^3 to lowest order in v. We argue that the F proportional to v^3 prediction results from an oversimplified treatment of the atom as a linear oscillator, and that F depends on v in just the way predicted by Scheel and Buhmann and Barton.