Fluctuational electrodynamics in and out of equilibrium

Abstract

Dispersion forces between neutral material bodies are due to fluctuations of the polarization of the bodies. For bodies in equilibrium these forces are often referred to as Casimir–Lifshitz forces. For bodies in relative motion, in addition to the Casimir–Lifshitz force, a lateral frictional force (“quantum friction”, in the zero temperature limit) comes into play. The widely accepted theory of the fluctuation-induced forces is based on the “fluctuational electrodynamics”, when the Maxwell equations are supplemented by random current sources responsible for the fluctuations of the medium polarization. The first part of our paper touches on some conceptual issues of the theory, such as the dissipation-less limit and the link between Rytov’s approach and quantum electrodynamics. We point out the problems with the dissipation-less plasma model (with its unphysical double pole at zero frequency) which still appears in the literature. The second part of the paper is devoted to “quantum friction”, in a broad sense, and it contains some novel material. In particular, it is pointed out that in weakly dissipative systems the friction force may not be a stationary process. It is shown, using an “exact” (nonperturbative) quantum treatment, that under appropriate conditions, an instability can occur when the kinetic energy (due to the relative motion between the bodies) is transformed into coherent radiation, exponentially growing in intensity (the instability gets eventually limited by nonlinear effects). We also discuss a setup when the two bodies are at rest but a constant electric current is flowing in one of the bodies. One may say that only the electron component of one body is dragged with respect to the other body, unlike the usual setup when the two bodies are in relative motion. Clearly, there are differences in the frictional forces between the two setups.