Casimir Friction in Terms of Moving Harmonic Oscillators: Equivalence Between Two Different Formulations

TL;DR

This paper demonstrates the equivalence of two formulations for calculating Casimir friction energy dissipation using moving harmonic oscillators, resolving apparent discrepancies and reinforcing the theoretical consistency at zero temperature.

Contribution

It shows that two different approaches to Casimir friction dissipation are physically equivalent, clarifying a potential contradiction in the theory.

Findings

The dissipation expressions are equivalent at T=0.

Resolves discrepancy between previous calculations.

Supports the consistency of Casimir friction theory.

Abstract

The Casimir friction problem can be dealt with in a simplified way by considering two harmonic oscillators moving with constant relative velocity. Recently we calculated the energy dissipation for such a case, [EPL {\bf 91}, 60003 (2010); Europ. Phys. J. D {\bf 61}, 335 (2011)]. A recent study of Barton [New J. Phys. {\bf 12}, 113044 (2010)] seemingly leads to a different result for the dissipation. If such a discrepancy really were true, it would imply a delicate difficulty for the basic theory of Casimir friction. In the present note we show that the expressions for the dissipation are in fact physically equivalent, at T=0.