Geometric origin of excess low-frequency vibrational modes in weakly connected amorphous solidsM. Wyart1, S. R. Nagel2 and T. A. Witten2
1 Service de Physique de l'Etat Condensé (CNRS URA 2464), DSM/DRECAM CEA Saclay, 91191 Gif-sur-Yvette, France
2 The James Frank Institute, The University of Chicago - Chicago, IL 60637, USA
received 5 April 2005; accepted in final form 6 September 2005
published online 23 September 2005
Glasses have an excess number of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature necessarily occurs in solids with low coordination. In particular, we analyze the density of normal-mode frequencies and the nature of the low-frequency normal modes of a recently simulated system (O'HERN C., SILBERT L. E., LIU A. J. and NAGEL S. R., Phys. Rev. E, 68 (2003) 011306) comprised of weakly compressed spheres at zero temperature. We account for the observed a) convergence of toward a non-zero constant as the frequency goes to zero, b) appearance of a low-frequency cutoff , and c) power law increase of with compression. We introduce a length scale l* which characterizes the vibrational modes that appear at .
81.05.Rm - Porous materials; granular materials.
82.70.-y - Disperse systems; complex fluids.
83.80.Fg - Granular solids.
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