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

Abstract

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 $\Sigma (k,z)\propto k^2{z}^{d/2}$ and not $\Sigma (k,z)\propto k^2{z}^{(d-2)/2}$, 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 $Z(t)\propto t^{(d+2)/2}$.

27 pages

Cited by in corpus (6)

• Non-Hermitian Euclidean random matrix theory
• Coherent-Potential approximation for diffusion and wave propagation in topologically disordered systems
• Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators
• Properties of stable ensembles of Euclidean random matrices
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Sound Attenuation in Glasses