Title: Finite-time scaling at the Anderson transition for vibrations in solids,
Abstract: 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.