Sparse phonon modes of a limit-periodic structure
Materials Science
2016-05-18 v1
Abstract
Limit-periodic structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. We study a ball and spring model with a limit-periodic pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to limit-periodic systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the limit-periodic structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.
Cite
@article{arxiv.1601.06175,
title = {Sparse phonon modes of a limit-periodic structure},
author = {Catherine Marcoux and Joshua E. S. Socolar},
journal= {arXiv preprint arXiv:1601.06175},
year = {2016}
}
Comments
10 pages, 13 figures