Finite-time scaling at the Anderson transition for vibrations in solids

A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame, exhibits an Anderson localization transition. To study this transition, we assume that the dynamical matrix of the network is given by a product of a sparse random matrix with real, independent, Gaussian-distributed non-zero entries and its transpose. A finite-time scaling analysis of system's response to an initial excitation allows us to estimate the critical parameters of the localization transition. The critical exponent is found to be $\nu = 1.57 \pm 0.02$ in agreement with previous studies of Anderson transition belonging to the three-dimensional orthogonal universality class.Comment: Revised manuscript. 8 pages, 5 figure

Anderson transition for elastic waves in three dimensions

We use two different fully vectorial microscopic models featuring nonresonant and resonant scattering, respectively, to demonstrate the Anderson localization transition for elastic waves in three-dimensional (3D) disordered solids. Critical parameters of the transition determined by finite-time and finite-size scaling analyses suggest that the transition belongs to the 3D orthogonal universality class. Similarities and differences between the elastic-wave and light scattering in strongly disordered media are discussed.Comment: A misprint in Eq. (21) was corrected. No other change