Anderson localization in Euclidean random matrices

CILIBERTI, S.; GRIGERA, T. S.; MARTÍN MAYOR, V.; PARISI, G.; VERROCCHIO, P.

PHYSICAL REVIEW B - CONDENSED MATTER AND MATERIALS PHYSICS

American Physical Society

Año: 2005 vol. 71 p. 153104 - 153104

0163-1829

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 exact on the random graph for the probability distribution function of the diagonal elements of the resolvent matrix, with a population dynamics algorithm (PDA). 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.