The vacuum energy for two cylinders one of which becoming large

TL;DR

This paper analyzes the asymptotic behavior of vacuum energy in a two-cylinder configuration, deriving explicit corrections as one cylinder's radius becomes large, with implications for quantum field theory in confined geometries.

Contribution

It provides the first explicit asymptotic expansion and next-to-leading order corrections for vacuum energy in a two-cylinder setup with one large radius.

Findings

Asymptotic expansion of vacuum energy for large cylinder radius.

Explicit calculation of next-to-leading order corrections.

Insights into vacuum energy behavior in cylindrical geometries.

Abstract

We consider the vacuum energy for a configuration of two cylinders and obtain its asymptotic expansion if the radius of one of these cylinders becomes large while the radius of the other one and their separation are kept fixed. We calculate explicitly the next-to-leading order correction to the vacuum energy for the radius of the other cylinder becoming large or small.