Incollection,
Localization behavior of vibrational modes in granular packings
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
An important research topic in the last few years has been the anomalous scaling of the properties of granular packings near the jamming point, resulting from the fact that at jamming, a granular packing is a marginal solid. We report on the first results for the localization behavior of vibrational modes of frictionless granular media as the jamming point is approached. All our data collapse within statistical errors onto a single curve, when properly rescaled with the system size and pressure. The localization length shows no signature of the nearness of the jamming point. Moreover, our results from level statistics show that modes whose localization length $\xi$ is larger than the linear system size $L$ interact, i.e. there is strong level repulsion due to the overlap of the modes, and they follow Wigner statistics. Also our results for modes with localization length $\xi<L$ show that they basically do not interact and follow Poisson statistics.
