Nonequilibrium Electromagnetic Fluctuations: Heat Transfer and Interactions

The Casimir force between arbitrary objects in equilibrium is related to scattering from individual bodies. We extend this approach to heat transfer and Casimir forces in nonequilibrium cases where each body, and the environment, is at a different temperature. The formalism tracks the radiation from each body and its scatterings by the other objects. We discuss the radiation from a cylinder, emphasizing its polarized nature, and obtain the heat transfer between a sphere and a plate, demonstrating the validity of proximity transfer approximation at close separations and arbitrary temperatures.

Figure 1

Heat radiation of a cylinder and a sphere of ${\mathrm{SiO}}_2$, as a function of $R$, normalized by the Stefan-Boltzmann result, at $T=300\mathrm{K}$. The horizontal line shows the radiation of a ${\mathrm{SiO}}_2$ plate. ${\lambda }_T$ and the smallest skin depth $\delta$ in the relevant frequency range are marked on the $R$ axis. For the cylinder, the contributions of the different polarizations are shown.

Figure 2

Heat transfer rate (in units of Stefan-Boltzmann’s law) from a room temperature plate to a sphere at $T=0$ of radius $R=5\mu \mathrm{m}$ (both ${\mathrm{SiO}}_2$), as a function of separation. The horizontal bar shows the limit of $d\to \infty$. The left inset shows the approach to PTA for the divergent terms in a one reflection approximation. The right inset shows the result at large separation as a function of $R$.