Abstract
A lattice boson model is used to study ordering phenomena in regular 2D arrays of superconductive mesoscopic granules, Josephson junctions and pores filled with superfluid helium. The phase diagram of the system, for when quantum fluctuations of both the phase and the local superfluid density are essential, is analysed both analytically and by the quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density is increased the boundary of the ordered superconducting state shifts to lower temperatures and at approaches its limiting position corresponding to negligible relative fluctuations of the moduli of the order parameter (as in an array of `macroscopic' granules). In the region of weak quantum fluctuations of phases, mesoscopic phenomena manifest themselves up to . The mean-field theory and functional integral -expansion results are shown to agree with those of quantum Monte Carlo calculations of the boson Hubbard model and its quasiclassical limit, the quantum XY-model.
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