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arXiv · 1709.05250

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

Y. M. Beltukov·S. E. Skipetrov
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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 $ν= 1.57 \pm 0.02$ in agreement with previous studies of Anderson transition belonging to the three-dimensional orthogonal universality class.

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Y. M. Beltukov, S. E. Skipetrov. 2017-11-08. Finite-time scaling at the Anderson transition for vibrations in solids. https://doi.org/10.1103/physrevb.96.174209

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