Localization behavior of vibrational modes in granular packingsZorana Zeravcic1, Wim van Saarloos1 and David R. Nelson2
1 Instituut - Lorentz, Universiteit Leiden - Postbus 9506, 2300 RA Leiden, The Netherlands
2 Department of Physics, Harvard University - Cambridge, MA 02138, USA
received 21 February 2008; accepted in final form 25 June 2008; published August 2008
published online 31 July 2008
We study the localization of vibrational modes of frictionless granular media. We introduce a new method, motivated by earlier work on non-Hermitian quantum problems, which works well both in the localized regime where the localization length is much less than the linear size L and in the regime when modes are extended throughout our finite system. Our very lowest frequency modes show "quasi-localized" resonances away from the jamming point; the spatial extent of these regions increases as the jamming point is approached, as expected theoretically. Throughout the remaining frequency range, our data show no signature of the nearness of the jamming point and collapse well when properly rescaled with the system size. Using Random Matrix Theory, we derive the scaling relation Ld/2 for the regime in d dimensions.
45.70.-n - Granular systems.
63.50.-x - Vibrational states in disordered systems.
71.23.An - Theories and models; localized states.
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