Casimir Friction Force and Energy Dissipation for Moving Harmonic Oscillators

TL;DR

This paper investigates Casimir friction between dielectric particles in relative motion using a microscopic statistical mechanics model, providing insights into energy dissipation and extending previous theories with a more general dissipation expression.

Contribution

It introduces a statistical-mechanical approach to Casimir friction, extending earlier work and deriving a general energy dissipation expression applicable beyond simple oscillator models.

Findings

Finite friction force at finite temperature

Zero force at zero temperature

Derived a general energy dissipation expression

Abstract

The Casimir friction problem for a pair of dielectric particles in relative motion is analyzed, utilizing a microscopic model in which we start from statistical mechanics for harmonically oscillating particles at finite temperature moving nonrelativistically with constant velocity. The use of statistical mechanics in this context has in our opinion some definite advantages, in comparison with the more conventional quantum electrodynamic description of media that involves the use of a refractive index. The statistical-mechanical description is physical and direct, and the oscillator model, in spite of its simplicity, is nevertheless able to elucidate the essentials of the Casimir friction. As is known, there are diverging opinions about this kind of friction in the literature. Our treatment elaborates upon, and extends, an earlier theory presented by us back in 1992. There we found a finite friction force at any finite temperature, whereas at zero temperature the model led to a zero force. As an additional development in the present paper we evaluate the energy dissipation making use of an exponential cutoff truncating the relative motion of the oscillators. For the dissipation we also establish a general expression that is not limited to the simple oscillator model.