Collective charge fluctuations and Casimir interactions for quasi one-dimensional metals

TL;DR

This paper studies the Casimir forces between metallic cylinders and plates, revealing how material properties influence interactions at various distances through numerical and analytical methods.

Contribution

It provides a comprehensive analysis of Casimir interactions for quasi-one-dimensional metals, including new insights into the dependence on material models and separation distances.

Findings

Large-distance interactions are independent of material properties for plasma models.

For Drude models, the interaction depends on dc conductivity and can become material-independent.

Numerical results align with analytical predictions and approach proximity force approximation at short distances.

Abstract

We investigate the Casimir interaction between two parallel metallic cylinders and between a metallic cylinder and plate. The material properties of the metallic objects are implemented by the plasma, Drude and perfect metal model dielectric functions. We calculate the Casimir interaction numerically at all separation distances and analytically at large separations. The large-distance asymptotic interaction between one plasma cylinder parallel to another plasma cylinder or plate does not depend on the material properties, but for a Drude cylinder it depends on the dc conductivity $\sigma$. At intermediate separations, for plasma cylinders the asymptotic interaction depends on the plasma wave length $\lambda_{\rm p}$ while for Drude cylinders the Casimir interaction can become independent of the material properties. We confirm the analytical results by the numerics and show that at short separations, the numerical results approach the proximity force approximation.