Mesoscopic Casimir forces in quantum vacuum

G. E. Volovik

Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland

L.D. Landau Institute for Theoretical Physics RAS, 117940 Moscow, Russia

PACS: 04.90.+e, 11.10.-z, 67.20.+k

**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 by the factor
larger than the
traditional value of the Casimir force given
by effective theory, where is the interatomic distance which plays the
role of the Planck length.