Abstract
Coulomb repulsion is taken into account to derive the thermodynamics of charged bosons in a random external potential. A simple analytical form of the partition function is proposed for the case of non-overlapping localized states (i.e. a small amount of disorder). The density of localized bosons and the specific heat show a peculiar non-uniform temperature dependence below the Bose - Einstein condensation temperature. The superfluid - Bose-glass phase diagram is discussed. A new phase is predicted which is a Bose glass at T = 0 but a superfluid at finite T.
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