Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering

Details Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering

2010-03-12

arxiv.org/abs/1003.2514v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

27 pages

Scientific paper

By calculating all terms of the high-density expansion of the 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 $\Sigma(k,z)\propto k^2z^{d/2}$ and not $\Sigma(k,z)\propto k^2z^{(d-2)/2}$, 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 $Z(t)\propto t^{(d+2)/2}$.

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