Stochastic Quantization and Casimir Forces: Pistons of Arbitrary Cross Section

TL;DR

This paper applies a stochastic quantization method to compute Casimir forces in arbitrary geometries, including finite pistons with various cross sections, considering quantum and thermal fluctuations, and deriving asymptotic expressions.

Contribution

It extends stochastic quantization techniques to calculate Casimir forces for pistons of arbitrary cross sections, providing new asymptotic formulas and detailed analysis for triangular geometries.

Findings

Derived asymptotic expressions at different temperature and distance regimes.

Analyzed Casimir forces for a piston with triangular cross section.

Described regularization of divergent stress tensor.

Abstract

Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplacian operator in the given geometry. Both quantum and thermal fluctuations are considered. Here we use such method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures and short and long distances are obtained. The case of a piston with triangular cross section is analysed in detail. The regularization of the divergent stress tensor is described.