The Casimir Forces in a Single Conducting Cylindrical Cavity

TL;DR

This paper calculates the Casimir forces inside a single conducting cylindrical cavity using Green functions and plasma frequency cutoff, finding repulsive forces at nanometer scales relevant for real materials.

Contribution

It introduces a method to compute Casimir energies inside a cylindrical cavity considering real conductors and neglecting external contributions, revealing repulsive forces.

Findings

Casimir forces inside the cavity are repulsive.

Forces are computed for nanometer-scale cavities made of real conductors.

The method accounts for realistic material properties and geometry.

Abstract

We want to study the Casimir effect for a single conducting microscopic cylindrical cavity. The mathematical technique is based on the Green function of the geometry of the inside of the cavity, and the integral regularization is based on the plasma frequency cutoff for real conductors. Using the symmetric electromagnetic energy-momentum tensor, in terms of four potential, the total Casimir energy for the inside of the Cavity is calculated. Neglecting the contribution of the external (outside of the cavity) Casimir energy based on the reason recently presented in [1], the forces experienced by the lateral surface of the cavity and its circular bases are calculated. The resulting expressions show that these forces are repulsive. The numerical computation is done for the real problem of a cavity with a basis of a radius in the same order of its height at the scale of 100 nanometers made of the best conducting materials already known.