Abstract
By calculating all terms of the high-density expansion of Euclidean random matrix theory (up to second-order in the inverse density) for the vibrational spectrum of a topologically disordered system, we show that the low-frequency behavior of the self-energy is given by Σ(k, z) ∝ k 2 z d/2 and not Σ(k, z) ∝ k 2 z (d−2)/2, as claimed previously. This implies the presence of Rayleigh scattering and long-time tails of the velocity autocorrelation function of the analogous diffusion problem of the form Z(t) ∝ t (d+2)/2.
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