Bose-Einstein condensation on inhomogeneous networks: Mesoscopic aspects versus thermodynamic limit

We study the filling of states in a pure hopping boson model on the comb lattice, a low-dimensional discrete structure where geometrical inhomogeneity induces Bose-Einstein condensation (BEC) at finite temperature. By a careful analysis of the thermodynamic limit on combs we show that, unlike the standard lattice case, BEC is characterized by a macroscopic occupation of a finite number of states with energy belonging to a small neighborhood of the ground state energy. Such a remarkable feature gives rise to an anomalous behavior in the large distance two-point correlation functions. Finally, we prove a general theorem providing the conditions for the pure hopping model to exhibit the standard behavior, i.e. to present a macroscopic occupation of the ground state only.