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VOLUME 73 (2001) | ISSUE 8 | PAGE 419
Mesoscopic Casimir forces in quantum vacuum
PACS: 04.90.+e, 11.10.-z, 67.20.+k
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 by the factor N^{1/3}\sim L/ a_{P} larger than the traditional value of the Casimir force given by effective theory, where a_{P}=\hbar/p_{
P} is the interatomic distance which plays the role of the Planck length.