Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 12: Poster I
DY 12.41: Poster
Tuesday, March 24, 2009, 14:30–16:30, P1A
Wave localization in complex networks with high clustering — •Lukas Jahnke1, Jan W. Kantelhardt1, Richard Berkovitz2, and Shlomo Havlin2 — 1Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany — 2Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
We study localization phenomena in complex optical networks. We find that strong clustering of links, i.e., a high probability of triadic closure, can induce a localization-delocalization quantum phase transition (Anderson-like transition) of coherent excitations. For example, the propagation of light wave-packets between two distant nodes of an optical network (composed of fibers and beam splitters) will be absent if the fraction of closed triangles exceeds a certain threshold. We suggest that such an experiment is feasible with current optics technology. We determine the corresponding phase diagram as a function of clustering coefficient and disorder for scale-free networks with different degree distributions characterized by an exponent lambda. Without disorder, we observe no phase transition for lambda<4, a quantum transition for lambda>4 and an additional distinct classical transition for lambda>4.5. Disorder reduces the critical clustering coefficient such that phase transitions occur for smaller lambda. Ref.: Jahnke, Kantelhardt, Berkovits, and Havlin, Phys. Rev. Lett. 101, 175702 (2008)