Correlated disorder and propagating modes in the frenkel-kontorova model

Jukka A. Ketoja, Indubala I. Satija

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

Abstract

The incommensurate Frenkel-Kontorova model in its pinned phase is shown to be equivalent to a system with correlated disorder. This correlated disorder appears as dimer-type “defects” on appropriately decimated lattices describing the phonon modes of the system. As a consequence of the special resonance condition where the reflected waves from two sites of the dimer undergo destructive interference, the decimated lattices exhibit Bloch-type phonon modes for energies that can be tuned by varying the nonlinearity parameter of the system. In a generalized two-parameter model, where the strength and the smoothness of the potential can be controlled independently, our study provides strong evidence of localization in a discrete quasiperiodic potential with an infinite number of steps. This localization boundary interwines with the parameter region exhibiting the Bloch-type states.

Original languageEnglish
Pages (from-to)9174-9184
Number of pages11
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume59
Issue number14
DOIs
Publication statusPublished - 1 Jan 1999
MoE publication typeNot Eligible

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Dimers
disorders
dimers
reflected waves
Defects
nonlinearity
interference
defects
energy
Statistical Models

Cite this

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Correlated disorder and propagating modes in the frenkel-kontorova model. / Ketoja, Jukka A.; Satija, Indubala I.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 59, No. 14, 01.01.1999, p. 9174-9184.

Research output: Contribution to journalArticleScientificpeer-review

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AB - The incommensurate Frenkel-Kontorova model in its pinned phase is shown to be equivalent to a system with correlated disorder. This correlated disorder appears as dimer-type “defects” on appropriately decimated lattices describing the phonon modes of the system. As a consequence of the special resonance condition where the reflected waves from two sites of the dimer undergo destructive interference, the decimated lattices exhibit Bloch-type phonon modes for energies that can be tuned by varying the nonlinearity parameter of the system. In a generalized two-parameter model, where the strength and the smoothness of the potential can be controlled independently, our study provides strong evidence of localization in a discrete quasiperiodic potential with an infinite number of steps. This localization boundary interwines with the parameter region exhibiting the Bloch-type states.

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