Long range Casimir force induced by transverse electromagnetic modes

TL;DR

This paper demonstrates that transverse electromagnetic modes induce a long-range Casimir force between conducting plates inside a cylindrical cavity, decaying as 1/a^2 and dominating at large distances, revealing a physical realization of the 1+1 dimensional Casimir effect.

Contribution

It shows that TEM modes produce a long-range Casimir force independent of plate area, dominating over TE and TM modes at large distances, and provides explicit calculations for cylindrical geometries.

Findings

TEM modes produce a 1/a^2 decay Casimir force.

TEM force dominates over TE and TM at large distances.

Explicit force calculations for cylindrical cavities.

Abstract

We consider the interaction of two perfectly conducting plates of arbitrary shape that are inside a non-simply connected cylinder with transverse section of the same shape. We show that the existence of transverse electromagnetic (TEM) modes produces a Casimir force that decays only as $1/a^2$, where $a$ is the distance between plates. The TEM force does not depend on the area of the plates and dominates at large distances over the force produced by the transverse electric (TE) and transverse magnetic (TM) modes, providing in this way a physical realization of the 1+1 dimensional Casimir effect. For the particular case of a coaxial circular cylindrical cavity, we compute the TE, TM and TEM contributions to the force, and find the critical distance for which the TEM modes dominate.