Mixing rules and the Casimir force between composite systems

TL;DR

This paper investigates how different effective medium approximations influence the calculation of Casimir-Lifshitz forces between composite slabs with metallic inclusions, highlighting the importance of approximation choice for accurate theoretical predictions.

Contribution

It compares various effective medium models for predicting Casimir forces in composite materials and discusses the impact of spectral representation on complex frequency analysis.

Findings

Choice of effective medium approximation significantly affects force calculations.

Spectral representation aids in accurate Wick rotation to complex frequencies.

Force predictions vary with filling fraction and separation distance.

Abstract

The Casimir-Lifshitz force is calculated between two inhomogeneous composite slabs, each made of a homogeneous matrix with spherical metallic inclusions. The effective dielectric function of the slabs is calculated using several effective medium approximations and we compare the resulting forces as a function of slab separation and filling fraction. We show that the choice of effective medium approximation is critical in making precise comparisons between theory and experiment. The role that the spectral representation of the effective medium plays in making a Wick rotation to the complex frequency axis is also discussed.