Linear response relations in fluctuational electrodynamics

Abstract

Near field radiative heat transfer and vacuum friction are just two instances of topics of technological and fundamental interest studied via the formalism of fluctuational electrodynamics. From the perspective of experiment and simulations, it is hard to precisely control and probe such nonequilibrium situations. Fluctuations in equilibrium are easier to measure, and typically can be related to non-equilibrium response functions by Green-Kubo relations. We consider a collection of arbitrary objects in vacuum, perturbed by changing the temperature or velocity of one object. Developing a method for computation of higher order correlation functions in fluctuational electrodynamics, we explicitly compare linear response and equilibrium fluctuations. We obtain a GreenKubo relation for the radiative heat transfer, as well as a closed formula for the vacuum friction in arbitrary geometries in the framework of scattering theory. We comment on the signature of the radiative heat conductivity in equilibrium fluctuations.

Green-Kubo relation for thermal radiation in non-reciprocal systems

“…We have verified that our results are in agreement with the corresponding expressions in Refs. [32,35]. Obviously, in global thermal equilibrium the total power emitted or radiated by object α or β vanishes as expected for equilibrium.…”

“…In such many body systems, it is still possible to establish a link between the heat flux between two objects surrounded by an arbitrary environment which can consist of many other objects and the equilibrium fluctuations in the many-body system as shown by Golyk et al [32] within the scattering approach. This link is given by the Kubo or Green-Kubo relation [32]. To be more precise, let us consider two compact objects of arbitrary material and shape placed within an arbitrary environment as sketched in Fig.…”

“…By making the assumption that the thermal radiation field has the Gauss property [39], these correlation functions can be expressed in terms of the second-order correlation function by virtue of the moment theorem [39]. Then by switching to frequency space we can express H αβ by [32] H αβ = 2Re…”

Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges

“…In addition, the quantum Casimir-Polder interaction between atoms and surfaces has been studied in a number of out of equilibrium contexts [20][21][22][23]. Here one can also study the evolution of a quantum state of the system which is not a stationary state, as well as the Casimir friction effect due to the motion of the atom [24,25]. These studies are more closely related to the one that will be presented here in that we study the evolution of the Casimir force in an initially out off equilibrium state to its equilibrium value.…”

Three-body radiation dynamics in systems with anisotropic nanoparticles

“…Several theories have been proposed to explain the heat transfer between simple particle geometries at nanoscale distances and have been widely used for two-body systems including parallel slabs 7-9 , a particle in front of a planar surface 3,10,11 ,two spheres [12][13][14][15][16] , and two anisotropic objects [17][18][19] . There are series of theoretical studies in recent years concerning the many body effects in the radiative heat transfer [20][21][22][23][24][25] . It is shown in many publications that the heat flux exchange between two objects can be remarkably enhanced in a three-body system with respect to a two-body system, thanks to many-body interactions.…”