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Pis'ma v Zh. Èksper. Teoret. Fiz., 2009, Volume 89, Issue 3, Pages 170–175 (Mi jetpl357)  

This article is cited in 2 scientific papers (total in 2 papers)

CONDENSED MATTER

$q$-breathers in discrete nonlinear schrödinger arrays with weak disorder

M. V. Ivanchenko

Department of Applied Mathematics, University of Leeds, LS2 9JT Leeds, United Kingdom

Abstract: Nonlinearity and disorder are key players in vibrational lattice dynamics, responsible for localization and delocalization phenomena. $q$-Breathers – periodic orbits in nonlinear lattices, exponentially localized in the reciprocal linear mode space – is a fundamental class of nonlinear oscillatory modes, currently found in disorder-free systems. In this paper we generalize the concept of $q$-breathers to the case of weak disorder, taking the Discrete Nonlinear Schrödinger chain as an example. We show that $q$-breathers retain exponential localization near the central mode, provided that disorder is sufficiently small. We analyze statistical properties of the instability threshold and uncover its sensitive dependence on a particular realization. Remarkably, the threshold can be intentionally increased or decreased by specifically arranged inhomogeneities. This effect allows us to formulate an approach to controlling the energy flow between the modes. The relevance to other model arrays and experiments with miniature mechanical lattices, light and matter waves propagation in optical potentials is discussed.

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English version:
Journal of Experimental and Theoretical Physics Letters, 2009, 89:3, 150–155

Bibliographic databases:

PACS: 05.45.-a, 63.20.-e
Received: 05.12.2008
Revised: 11.01.2009
Language: English

Citation: M. V. Ivanchenko, “$q$-breathers in discrete nonlinear schrödinger arrays with weak disorder”, Pis'ma v Zh. Èksper. Teoret. Fiz., 89:3 (2009), 170–175; JETP Letters, 89:3 (2009), 150–155

Citation in format AMSBIB
\Bibitem{Iva09}
\by M.~V.~Ivanchenko
\paper $q$-breathers in discrete nonlinear schr\"{o}dinger arrays with weak disorder
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2009
\vol 89
\issue 3
\pages 170--175
\mathnet{http://mi.mathnet.ru/jetpl357}
\transl
\jour JETP Letters
\yr 2009
\vol 89
\issue 3
\pages 150--155
\crossref{https://doi.org/10.1134/S0021364009030114}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000264923100011}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-64349089690}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Krimer D.O., Flach S., “Statistics of wave interactions in nonlinear disordered systems”, Physical Review E, 82:4, Part 2 (2010), 046221  crossref  adsnasa  isi  elib  scopus
    2. JETP Letters, 92:6 (2010), 365–369  mathnet  crossref  isi
  •       Pis'ma v Zhurnal ksperimental'noi i Teoreticheskoi Fiziki
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