Geometric origin of excess lowfrequency vibrational modes in weakly connected amorphous solids
Abstract
Glasses have an excess number of lowfrequency 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 D(ω) of normalmode frequencies ω and the nature of the lowfrequency 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 D(ω) toward a nonzero constant as the frequency goes to zero, b) appearance of a lowfrequency cutoff ω*, and c) power law increase of ω* with compression. We introduce a length scale l* which characterizes the vibrational modes that appear at ω*.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 November 2005
 DOI:
 10.1209/epl/i2005102455
 arXiv:
 arXiv:condmat/0409687
 Bibcode:
 2005EL.....72..486W
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 4 pages, 2 figures. Argument rewritten, identical results