# Localization Behavior of Vibrational Modes in Granular Packings

 Title: Localization Behavior of Vibrational Modes in Granular Packings Author: Saarloos, Wim; Zeravcic, Zorana; Nelson, David R. Note: Order does not necessarily reflect citation order of authors. Citation: Zeravcic, Zorana, Wim Saarloos, and David Nelson. 2008. Localization behavior of vibrational modes in granular packings. Europhysics Letters 83(4): 44001. Full Text & Related Files: 0802.3440v2.pdf (833.4Kb; PDF) Abstract: 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 $$\xi$$ is much less than the linear size $$L$$ and in the regime $$\xi \gsim L$$ 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 $$\xi \sim L^{d/2}$$ for the regime $$\xi \gg L$$ in $$d$$ dimensions. Published Version: doi:10.1209/0295-5075/83/44001 Other Sources: http://arxiv.org/abs/0802.3440v2 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8160707 Downloads of this work: