Mesoscopic Casimir forces in quantum vacuum
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Traditionally, it is assumed that the Casimir vacuum pressure does not depend on the ultraviolet cutoff. There are, however, some arguments that the effect actually depends on the regularization procedure and thus on trans-Planckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on 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 elements comprising the quantum vacuum). The finite-N effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic fluctuations of the Casimir force in a system with linear dimension L is a factor of N1/3∼L/a p larger than the traditional value of the Casimir force given by effective theory, where a p =ℏ/p p is the interatomic distance which plays the role of the Planck length.
PACS numbers67.20.+k 11.10.−z
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