Density of states in random lattices with translational invariance

Details Density of states in random lattices with translational invariance Density of states in random lattices with translational invariance

2010-11-12

arxiv.org/abs/1011.2955v2

JETP Letters, 2011, Vol. 93, No. 10, pp. 598-602

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1134/S002136401110002X

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).

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