Casimir Friction Force and Energy Dissipation for Moving Harmonic Oscillators. II

TL;DR

This paper extends a model of two oscillators in relative motion to second order in energy change, confirming previous results and showing finite friction at non-zero temperatures but zero friction at zero temperature.

Contribution

It introduces a second-order energy change analysis for a two-oscillator Casimir friction model using first-order perturbation theory, confirming earlier findings.

Findings

Friction force is finite at finite temperatures.

Friction force vanishes at zero temperature for constant velocity motion.

Results align with previous theoretical approaches.

Abstract

This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in Europhys. Lett. 91, 60003 (2010)). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is finite at finite temperatures, whereas in the case of two oscillators moving with constant relative velocity the force becomes zero at zero temperature, due to slowly varying coupling.