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| VOLUME 89 | ISSUE 3 |
PAGE 170
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| q-breathers in discrete nonlinear schrödinger arrays with weak disorder
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M. V. Ivanchenko
Department of Applied Mathematics, University of Leeds, LS2 9JT Leeds, United Kingdom
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PACS: 05.45.-a, 63.20.-e
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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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