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Brillouin and boson peaks in glasses from vector Euclidean random matrix theory

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Ciliberti, S. and Grigera, T.S. and Martín Mayor, Víctor and Parisi, G. and Verrocchio, P. (2003) Brillouin and boson peaks in glasses from vector Euclidean random matrix theory. Journal of chemical physics, 119 (16). pp. 8577-8591. ISSN 0021-9606

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Official URL: http://dx.doi.org/10.1063/1.1610439




Abstract

A simple model of harmonic vibrations in topologically disordered systems, such as glasses and supercooled liquids, is studied analytically by extending Euclidean random matrix theory to include vector vibrations. Rather generally, it is found that (i) the dynamic structure factor shows soundlike Brillouin peaks whose longitudinal/transverse character can only be distinguished for small transferred momentum, p; (ii) the model presents a mechanical instability transition at small densities, for which scaling laws are analytically predicted and confirmed numerically; (iii) the Brillouin peaks persist deep into the unstable phase, the phase transition being noticeable mostly in their linewidth; (iv) the Brillouin linewidth scales like p^(2) in the stable phase, and like p in the unstable one. The analytical results are checked numerically for a simple potential. The main features of glassy vibrations previously deduced from scalar are not substantially altered by these new results.


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© 2003 American Institute of Physics. We are indebted to Giancarlo Ruocco, Oreste Pilla, and Gabriele Viliani for helpful discussions. V.M.-M. is a Ramón y Cajal research fellow (MCyT, Spain). P.V. acknowledges financial support from the European Union through its Human Potential Program (Contract HPRN-CT-2002-00307, DYGLAGEMEM network). This work has been partly financially supported by MCyT Research Contracts FPA2001- 1813 and FPA2000-0956.

Uncontrolled Keywords:Instantaneous normal-modes; Dynamical structure factor; Liquid-state dynamics; X-ray-scattering; Vibrational excitations; Supercooled liquids; Disordered-systems; Potential-energy; Vitreous silica; Molecular-dynamics.
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:46431
Deposited On:09 Mar 2018 09:31
Last Modified:09 Mar 2018 09:31

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