Mesoscopic Casimir forces from effects of discrete particle number in the quantum vacuum

TL;DR

This paper demonstrates that mesoscopic effects in condensed matter systems cause Casimir forces to depend on microscopic particle number, challenging the assumption of ultraviolet cut-off independence and highlighting the influence of trans-Planckian physics.

Contribution

It provides a condensed matter example showing how finite particle number effects lead to mesoscopic fluctuations in Casimir forces, linking microscopic physics to macroscopic vacuum phenomena.

Findings

Mesoscopic fluctuations of Casimir force are larger by N^{1/3} than traditional predictions.

Casimir pressure depends on microscopic physics due to finite-N effects.

Finite particle number effects cause observable mesoscopic variations in vacuum pressure.

Abstract

Traditionally it is assumed that the Casimir vacuum pressure does not depend on the ultraviolet cut-off. There are, however, some arguments that the effect actually depends on the regularization procedure and thus on the trans-Planckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on the microscopic (correspondingly trans-Planckian) physics due to the mesoscopic finite-N effects, where N is the number of bare particles in condensed matter (or correspondingly the number of the elements comprising the quantum vacuum). The finite-N effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic flustuations of the Casimir force in a system with linear dimension L is larger by the factor N^{1/3}\sim L/a than the traditional value of the Casimir force given by effective theory, where a is the interatomic distance which plays the role of the Planck length.