Scaling Planck's law: a unified approach to the Casimir effect and radiative heat-conductance in nanogaps

Abstract

Using Planck's law from an innovative point of view brings about the possibility to understand the common origin of the repulsive Casimir thermal pressure and the heat exchange in nanogaps. Based on a scale transformation, a procedure that removes divergences of the energy density, we prove the validity of Planck's law to describe confined thermal radiation properties in nanoscale gaps. This scaling involves a configurational temperature obtained from Wien's displacement law and having an entropic origin. We derive analytical expressions for the Casimir thermal pressure as well as for the heat conductance. Comparison of our results with experimental data shows a remarkable agreement.