Abstract
In this chapter we consider the role played by Anderson localization in transport through complex networks, for example, an optical network. The network is described by a tight binding Hamiltonian, which may be used to determine the properties of the Anderson transition according to the statistical properties of its eigenvalues. The Anderson transition properties of different complex networks will be studied, emphasizing the role played by clustering on the localization of waves. We shall show that new complex topologies lead to novel physics, specifically clustering may lead to localization.
MSC2000 Primary 05C80; Secondary 90B18, 90B15, 05C50, 05C82.
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The N dependence is well established [35] but the C 0 dependence seems to be unexplored. Our data for N up to 105 suggest \(\ln a \propto {\left ({C}_{0} - {C}_{0,c}\right )}^{-{\nu }_{c}}\). Since C 0, q < C 0, c, a and thus L depend weakly on C 0 at the quantum transition.
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Berkovits, R., Jahnke, L., Kantelhardt, J.W. (2011). Wave Localization on Complex Networks. In: Dehmer, M., Emmert-Streib, F., Mehler, A. (eds) Towards an Information Theory of Complex Networks. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4904-3_4
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