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arXiv · 1601.06175

Sparse phonon modes of a limit-periodic structure

Catherine Marcoux·Joshua E. S. Socolar
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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.

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Catherine Marcoux, Joshua E. S. Socolar. 2016-01-22. Sparse phonon modes of a limit-periodic structure. https://doi.org/10.1103/physrevb.93.174102

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