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

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.

LaTeX file, 13 pages, no figures, submitted to JETP Letters

References in corpus (5)

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• When radiative corrections are finite but undetermined
• Casimir Energy for Spherical boundaries
• On the Zero-Point Energy of a Conducting Spherical Shell
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Cited by in corpus (5)

• Casimir effect in a one-dimensional gas of free fermions
• Phonon-mediated Casimir interaction between finite mass impurities
• Fermionic Casimir Effect in Case of Andreev Reflection
• T-matrix approach to the phonon-mediated Casimir interaction
• On the corrections to the Casimir effect depending on the resolution of measurement