Diffusion of vibrations in disordered systems
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We consider diffusion of vibrations in random lattices with translational invariance. Above the frequency ωIR corresponding to the Ioffe-Regel crossover (and depending on the strength of disorder), phonons cannot propagate through the lattice and transfer energy. At the same time, most of the vibrations in this range are not localized. We show that these delocalized excitations are similar to diffusons introduced by P. B. Allen, J. L. Feldman, J. Fabian, and F. Wooten (see, e.g., Phil. Mag. B 79, 1715 (1999)) to describe heat transport in glasses. In this range the energy in the lattice is transferred by means of diffusion of vibrational excitations. We have calculated the diffusivity of the modes D(ω) using both the direct numerical solution of Newton equations and the Edwards-Thouless formula. It is nearly constant above ωIR and goes to zero at the localization threshold.
KeywordsJETP Letter Vibrational Excitation Vibrational Property Dynamical Matrix Participation Ratio
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