Wave Localization in Complex Networks with High Clustering

Jahnke, Lukas; Kantelhardt, Jan W.; Berkovits, Richard; Havlin, Shlomo

doi:10.1103/physrevlett.101.175702

Cited by 50 publications

(49 citation statements)

References 35 publications

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“…The transition from Poisson to Wigner-Dyson in the spectral statistics has also been reported for adjacency matrices corresponding to other complex network models in Refs. [30][31][32][33][34][35][36][37].…”

Section: Erdős-rényi Fully Random Networkmentioning

confidence: 99%

Universality in the spectral and eigenfunction properties of random networks

et al. 2015

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By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution P (s) and the entropic eigenfunction localization length of the adjacency matrices of Erdős-Rényi (ER) fully random networks are universal for fixed average degree ξ ≡ αN (α and N being the average network connectivity and the network size, respectively). We also demonstrate that Brody distribution characterizes well P (s) in the transition from α = 0, when the vertices in the network are isolated, to α = 1, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks.

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Section: Erdős-rényi Fully Random Networkmentioning

confidence: 99%

Universality in the spectral and eigenfunction properties of random networks

et al. 2015

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“…Quantum critical phenomena also might depend on the topology of the underlying lattice as it has been shown for Bose-Einstein condensation in heterogeneous networks [17]. Although large attention has been devoted to classical critical phenomena on scale-free networks, the behavior of quantum critical phenomena on scale-free networks has just started to be investigated.In particular the Anderson localization [18,19] was studied in complex networks showing that by modulating the clustering coefficient of the …”

mentioning

confidence: 99%

“…In particular the Anderson localization [18,19] was studied in complex networks showing that by modulating the clustering coefficient of the…”

mentioning

confidence: 99%

Phase diagram of the Bose-Hubbard model on complex networks

Halu¹,

Ferretti²,

Vezzani³

et al. 2012

EPL

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-Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last decade. Here we show that the phase diagram of the Bose-Hubbard model, an exclusively quantum mechanical phase transition, also changes significantly when defined on random scale-free networks. We present a mean-field calculation of the model in annealed networks and we show that when the second moment of the average degree diverges the Mott-insulator phase disappears in the thermodynamic limit. Moreover we study the model on quenched networks and we show that the Mott-insulator phase disappears in the thermodynamic limit as long as the maximal eigenvalue of the adjacency matrix diverges. Finally we study the phase diagram of the model on Apollonian scale-free networks that can be embedded in 2 dimensions showing the extension of the results also to this case.Introduction. -Recently great attention [1, 2] has been addressed to critical phenomena unfolding on complex networks. In this context it has been observed that the topology of the networks might significantly change the phase diagram of dynamical processes. For example when networks have a scale-free degree distribution P (k) ∼ k −λ and the second moment k 2 diverges with the network size, i.e. λ ∈ (2, 3] the Ising model [3][4][5][6], the percolation phase transition [7,8] and the epidemic spreading dynamics on annealed networks [9] are strongly affected. Moreover the spectral properties of the networks drive the epidemic spreading on quenched networks [10,11], the synchronization stability [12,13], the critical behavior of O(N ) models [14,15] and the critical fluctuations of an Ising model on spatial scale-free networks [16]. Quantum critical phenomena also might depend on the topology of the underlying lattice as it has been shown for Bose-Einstein condensation in heterogeneous networks [17]. Although large attention has been devoted to classical critical phenomena on scale-free networks, the behavior of quantum critical phenomena on scale-free networks has just started to be investigated.In particular the Anderson localization [18,19] was studied in complex networks showing that by modulating the clustering coefficient of the

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“…In fact, the localization phenomenon could be induced by strong disorder in quantum complex networks. For example, Jahnke et al [23] Accuracy ratio p a as a function of t for several real complex networks. The horizontal axis is an index n with t = 0.001n.…”

Section: Reduction and Heuristic Estimatementioning

confidence: 99%

“…A fresh view of the application of our method emerges on considering quantum optical communication networks. Such an optical network may be considered in the form of a graph where edges represent optical fibers (or waveguides) and nodes represent optical units (essentially beam splitters) [23] which can redistribute incoming waves into outgoing fibers. The physical entity we choose here is photons or light wave packets.…”

Section: Reduction and Heuristic Estimatementioning

confidence: 99%