Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects

TL;DR

This paper derives trace formulae for non-equilibrium heat radiation, transfer, and Casimir interactions among arbitrary objects, providing a basis-independent framework and illustrating with examples like spheres and plates.

Contribution

It introduces a basis-independent trace formula approach for non-equilibrium electromagnetic interactions among arbitrary objects, extending previous equilibrium results.

Findings

Heat radiation of a single object is positive.

Heat transfer occurs from hotter to colder bodies and is symmetric upon temperature exchange.

A hot nano-sphere can levitate above a plate due to non-equilibrium forces.

Abstract

We present a detailed derivation of heat radiation, heat transfer and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal non-equilibrium. The results can be expressed as basis-independent trace formulae in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave-expansions, we transform the results for radiation, transfer and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nano-spheres is typically invalid. We derive asymptotic formulae for heat transfer and non-equilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nano-sphere can levitate above a plate with the repulsive non-equilibrium force overcoming gravity -- an effect that is not due to radiation pressure.