Application of the Lifshitz theory to poor conductors

TL;DR

This paper extends the Lifshitz theory to poor conductors by incorporating nonlocal dielectric responses, accounting for finite screening and relaxation effects, and compares predictions with recent experimental data.

Contribution

It generalizes the Lifshitz formula for dispersive forces to include nonlocal effects in poor conductors, ensuring a self-consistent theory at low temperatures.

Findings

Casimir-Lifshitz entropy vanishes linearly with temperature for degenerate plasma.

Entropy scales as temperature squared for nondegenerate plasma.

The theory aligns with recent experimental observations.

Abstract

The Lifshitz formula for the dispersive forces is generalized to the materials, which cannot be described with the local dielectric response. Principal nonlocality of poor conductors is related with the finite screening length of the penetrating field and the collisional relaxation; at low temperatures the role of collisions plays the Landau damping. The spatial dispersion makes the theory self consistent. Our predictions are compared with the recent experiment. It is demonstrated that at low temperatures the Casimir-Lifshitz entropy disappears as $T$ in the case of degenerate plasma and as $T^2$ for the nondegenerate one.