Sparse phonon modes of a limit-periodic structure

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Marcoux, C; Socolar, JES

Published Date

  • May 1, 2016

Published In

Volume / Issue

  • 93 / 17

Chapter

  • 174102

Published By

International Standard Serial Number (ISSN)

  • 0163-1829

Digital Object Identifier (DOI)

  • 10.1103/PhysRevB.93.174102