Asymptotic behavior of the density of states on a random lattice

Details Asymptotic behavior of the density of states on a random lattice Asymptotic behavior of the density of states on a random lattice

2004-09-08

arxiv.org/abs/cond-mat/0409212v2

J. Phys. A: Math. Gen., vol 38 (2005) L57-L65

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 2 figures

Scientific paper

10.1088/0305-4470/38/5/L02

We study the diffusion of a particle on a random lattice with fluctuating local connectivity of average value q. This model is a basic description of relaxation processes in random media with geometrical defects. We analyze here the asymptotic behavior of the eigenvalue distribution for the Laplacian operator. We found that the localized states outside the mobility band and observed by Biroli and Monasson (1999, J. Phys. A: Math. Gen. 32 L255), in a previous numerical analysis, are described by saddle point solutions that breaks the rotational symmetry of the main action in the real space. The density of states is characterized asymptotically by a series of peaks with periodicity 1/q.

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