Computation of Casimir forces for dielectrics or intrinsic semiconductors based on the Boltzmann transport equation

TL;DR

This paper develops a classical Boltzmann transport equation-based method to compute Casimir forces between dielectrics and semiconductors with low charge carrier density, addressing thermodynamic consistency and linking to spatial dispersion models.

Contribution

It introduces a detailed frequency-dependent reflection amplitude calculation within the Boltzmann transport framework for Casimir force computation, ensuring thermodynamic consistency.

Findings

The theory satisfies the Nernst theorem of thermodynamics.

Derived explicit frequency-dependent reflection amplitudes.

Connected Boltzmann transport approach to spatial dispersion models.

Abstract

The interaction between drifting carriers and traveling electromagnetic waves is considered within the context of the classical Boltzmann transport equation to compute the Casimir-Lifshitz force between media with small density of charge carriers, including dielectrics and intrinsic semiconductors. We expand upon our previous work [Phys. Rev. Lett. {\bf 101}, 163203 (2008)] and derive in some detail the frequency-dependent reflection amplitudes in this theory and compute the corresponding Casimir free energy for a parallel plate configuration. We critically discuss the the issue of verification of the Nernst theorem of thermodynamics in Casimir physics, and explicity show that our theory satisfies that theorem. Finally, we show how the theory of drifting carriers connects to previous computations of Casimir forces using spatial dispersion for the material boundaries.