Publication: Anderson localization in Euclidean random matrices
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2005-04-11
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American Physical Society
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Abstract
We study the spectra and localization properties of Euclidean random matrices defined on a random graph. We introduce a powerful method to find the density of states and the localization threshold in topologically disordered soff-latticed systems. We solve numerically an equation sexact on the random graphd for the probability distribution function of the diagonal elements of the resolvent matrix, with a population dynamics algorithm sPDAd. We show that the localization threshold can be estimated by studying the stability of a population of real resolvents under the PDA. An application is given in the context of the instantaneous normal modes of a liquid.
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© 2005 The American Physical Society. We acknowledge partial support from MCyT, Spain (Grants No. FPA2001-1813, No. FPA2000-0956, and No. BFM2003-08532-C03) and ANPCyT, Argentina. S.C. was supported by the ECHP program (Grant No. HPRN-CT2002-00307). V.M.-M. was supported by the Ramón y Cajal program, and P.V. by the European Commission (Grant No. MCFI-2002-01262). T.S.G. was supported by CONICET (Argentina).