Publications [#311986] of Joshua Socolar
- Marcoux, C; Socolar, JES, Sparse phonon modes of a limit-periodic structure,
Physical Review. B, Condensed Matter, vol. 93 no. 17
(May, 2016), American Physical Society, ISSN 0163-1829 [PhysRevB.93.174102], [doi]
(last updated on 2019/04/18)
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.