  Quantum fluctuations of the phases of the order parameter in 2D arrays of
mesoscopic Josephson junctions and their effect on the destruction of
superconductivity in the system are investigated by means of a quantum-cosine
model that is free of the incorrect application of the phase operator. The
proposed model employs trigonometric phase operators and makes it possible to
study arrays of small superconducting granules, pores filled with superfluid
helium, or Josephson junctions in which the average number of particles $n_0$
(effective bosons, He atoms, and so on) is small, and the standard approach
employing the phase operator and the particle number operator as conjugate ones
is inapplicable. There is a large difference in the phase diagrams between
arrays of macroscopic and mesoscopic objects for $n_0 < 5$ and $U<J$ ($U$ is
the characteristic interaction energy of the particle per granule and $J$ is
the Josephson coupling constant). Reentrant superconductivity phenomena are
discussed.
