Casimir Friction Force for Moving Harmonic Oscillators

Abstract

Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use a statistical-mechanical description where time-dependent correlations are involved. This description is physical and direct, and, in spite of its simplicity, is able to elucidate the essentials of the problem. This treatment elaborates upon, and extends, an earlier theory of ours back in 1992. The energy change ∆E turns out to be finite in general, corresponding to a finite friction force. In the limit of zero temperature the formalism yields, however, ∆E → 0, this being due to our assumption about constant velocity, meaning slowly varying coupling. For couplings varying more rapidly, there will also be a finite friction force at T = 0. As second part of our work, we consider the friction problem using time-dependent perturbation theory. The dissipation, basically a second order effect, is obtainable with the use of first order theory, the reason being the absence of cross terms due to uncorrelated phases of eigenstates. The third part of the present paper is to demonstrate explicitly the equivalence of our results with those recently obtained by Barton (2010); this being not a trivial task since the formal results are seemingly quite different from each other.

The Reality of Casimir Friction

“…One way is to apply methods from quantum statistical mechanics to the system of relatively moving harmonic oscillators, in general at a finite temperature T. This is the method that two of us have used repeatedly in previous recent investigations [46][47][48][49][50][51][52][53]; cf. also the earlier papers [26,27] where the basis of the formalism was laid.…”

Casimir friction between polarizable particle and half-space with radiation damping at zero temperature

“…A number of papers from the last 5 years are listed in Refs. [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. The research literature is quite diversified; some papers have focused on the complicated situation where the relative velocity is relativistic and even necessitating the inclusion of Cherenkov-like effects.…”

Casimir Friction between Dense Polarizable Media

“…We claim that such a strategy, formally perhaps simpler than field-theoretical methods, is actually quite powerful. We have used this method repeatedly in previous recent investigations [15][16][17][18][19]; cf., also the earlier papers [20,21] in which the foundations of the method were spelled out. The essence of the method is to generalize the statistical mechanical Kubo formalism to time-dependent cases.…”

“…For reasons of readability, we begin in the next section by summarizing essential points of the theory for dilute media [18,19]. Then, after giving an account of Fourier methods in Section 3, we embark, as mentioned, on the general case of finite particle density in Section 4.…”

“…For reasons of readability we begin in the next section by summarizing essential points of the theory for dilute media [18,19]. Then, after giving an account of Fourier methods in Sect.…”