Landauer's formula breakdown for radiative heat transfer and non-equilibrium Casimir forces

TL;DR

This paper derives explicit formulas for non-equilibrium Casimir forces and radiative heat transfer between finite-thickness plates, revealing how thickness influences these phenomena and challenging the universal applicability of Landauer's formula.

Contribution

It provides a first-principles analysis of the impact of plate thickness on non-equilibrium Casimir forces and heat transfer, including conditions where Landauer's formula applies.

Findings

Plate thickness affects the convergence to infinite-thickness limits.

Landauer's formula is not universally applicable to all contributions.

Thickness-dependent behaviors enable thermal shielding and tunable heat transfer.

Abstract

In this work we analyze the incidence of the plates' thickness on the Casimir force and radiative heat transfer for a configuration of parallel plates in a non-equilibrium scenario, relating to Lifshitz's and Landauer's formulas. From a first-principles canonical quantization scheme for the study of the matter-field interaction, we give closed-form expressions for the non-equilibrium Casimir force and the heat transfer between plates of thickness $d_{\rm L},d_{\rm R}$. We distinguish three different contributions to the Casimir force and to the heat transfer in the general non-equilibrium situation: two associated to each of the plates, and one to the initial state of the field. We analyze the dependence of the Casimir force and heat transfer with the plate thickness (setting $d_{\rm L}=d_{\rm R}\equiv d$), showing the scale at which each magnitude converges to the value of infinite thickness ($d\rightarrow+\infty$) and how to correctly reproduce the non-equilibrium Lifshitz's formula. For the heat transfer, we show that Landauer's formula does not apply to every case (where the three contributions are present), but it is correct for some specific situations. We also analyze the interplay of the different contributions for realistic experimental and nanotechnological conditions, showing the impact of the thickness in the measurements. For small thickness (compared to the separation distance), the plates act to decrease the background blackbody flux, while for large thickness the heat is given by the baths' contribution only. The combination of these behaviors allows for the possibility of having a tunable minimum in the heat transfer that is experimentally attainable and observable for metals, and also of having vanishing heat flux in the gap when those difference are of opposite signs (thermal shielding). These features turns out to be relevant for nanotechnological applications.