TY - JOUR

T1 - Wave localization in complex networks with high clustering

AU - Jahnke, Lukas

AU - Kantelhardt, Jan W.

AU - Berkovits, Richard

AU - Havlin, Shlomo

PY - 2008/10/23

Y1 - 2008/10/23

N2 - We show that strong clustering of links in complex networks, 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 of different degree distributions P(k)∼k-λ. Without disorder, we observe no phase transition for λ<4, a quantum transition for λ>4, and an additional distinct classical transition for λ>4.5. Disorder reduces the critical clustering coefficient such that phase transitions occur for smaller λ.

AB - We show that strong clustering of links in complex networks, 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 of different degree distributions P(k)∼k-λ. Without disorder, we observe no phase transition for λ<4, a quantum transition for λ>4, and an additional distinct classical transition for λ>4.5. Disorder reduces the critical clustering coefficient such that phase transitions occur for smaller λ.

UR - http://www.scopus.com/inward/record.url?scp=55049133078&partnerID=8YFLogxK

U2 - 10.1103/physrevlett.101.175702

DO - 10.1103/physrevlett.101.175702

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AN - SCOPUS:55049133078

SN - 0031-9007

VL - 101

JO - Physical Review Letters

JF - Physical Review Letters

IS - 17

M1 - 175702

ER -