Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks

Details Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks

2001-04-19

arxiv.org/abs/cond-mat/0104365v2

J. Phys A 35 (2002) 1245-1252

Physics

Condensed Matter

Statistical Mechanics

4 pages, 10 figures

Scientific paper

10.1088/0305-4470/35/5/308

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. We prove that the presence of hidden states in the lowest region of the spectrum is the necessary and sufficient condition for condensation in low dimension (spectral dimension $\bar{d}\leq 2$), while it is shown that BEC always occurs for $\bar{d}>2$.

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