Bose Einstein-Condensation and macroscopic filling of states on low dimensional complex networks
Alessandro Vezzani


Abstract
Topological inhomogeneity gives rise to spectral anomalies that can induce Bose-Einstein Condensation (BEC) in low dimensional systems. These anomalies consist in energy regions composed of an infinite number of states with vanishing weight in the thermodynamic limit (hidden states). Here we present a rigorous result giving the most general conditions for BEC on complex networks. Furthermore we focus our attention on the comb graph the typical low dimensional discrete structure presenting BEC at finite temperature. By a careful analysis of the thermodynamic limit 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. Finally, we prove a general theorem providing the conditions for the pure hopping model to exhibit the standard behaviour, i.e. to present a macroscopic occupation of the ground state only.

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Elenco dei partecipanti al convegno di Bari.

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