Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-05-23
J Chem Phys 119, 8577 (2003)
Physics
Condensed Matter
Disordered Systems and Neural Networks
15 postscript figures
Scientific paper
10.1063/1.1610439
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 sound-like 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 square 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 ERMT are not substantially altered by these new results.
Ciliberti Stefano
Grigera Tomas S.
Martin-Mayor Victor
Parisi Giorgio
Verrocchio Paolo
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