Casimir-Lifshitz force between moving plates at different temperatures

TL;DR

This paper extends the understanding of the Casimir-Lifshitz force to moving plates at different temperatures, revealing both perpendicular and lateral force components influenced by motion and thermal radiation.

Contribution

It generalizes previous zero-temperature models to include temperature differences and motion, deriving new force components and analyzing their physical implications.

Findings

Perpendicular Casimir-Lifshitz force includes quantum vacuum and thermal contributions.

Thermal radiation induces a lateral force component absent in static cases.

Zero-temperature limit confirms no quantum-vacuum friction between plates.

Abstract

The zero-temperature Casimir-Lifshitz force between two plates moving parallel to each other at arbitrary constant speed was found in [New J. Phys. 11, 033035 (2009)]. The solution is here generalized to the case where the plates are at different temperatures. The Casimir-Lifshitz force is obtained by calculating the electromagnetic stress tensor, using the method employed by Antezza et al. [Phys. Rev. A 77, 022901 (2008)] for non-moving plates at different temperatures. The perpendicular force on the plates has contributions from the quantum vacuum and from the thermal radiation; both of these contributions are influenced by the motion. In addition to the perpendicular force, thermal radiation from the moving plates gives rise to a lateral component of the Casimir-Lifshitz force, an effect with no quantum-vacuum contribution. The zero-temperature results are reproduced, in particular the non-existence of a quantum-vacuum friction between the plates.