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Nonlinear Sciences > Chaotic Dynamics

arXiv:2103.11041 (nlin)
[Submitted on 19 Mar 2021 (v1), last revised 11 May 2021 (this version, v2)]

Title:Chaos and localization in the Discrete Nonlinear Schrödinger Equation

Authors:Stefano Iubini, Antonio Politi
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Abstract:We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schrödinger equation. This nonintegrable model, ubiquitous in several fields of physics, describes the behavior of an array of coupled complex oscillators with a local nonlinear potential. We explore the Lyapunov spectrum for different values of the energy density, finding that the maximal value of the Kolmogorov-Sinai entropy is attained at infinite temperatures. Moreover, we revisit the dynamical freezing of relaxation to equilibrium, occurring when large localized states (discrete breathers) are superposed to a generic finite-temperature background. We show that the localized excitations induce a number of very small, yet not vanishing, Lyapunov exponents, which signal the presence of extremely long characteristic time-scales. We widen our analysis by computing the related Lyapunov covariant vectors, to investigate the interaction of a single breather with the various degrees of freedom.
Comments: 7 pages, 7 figures
Subjects: Chaotic Dynamics (nlin.CD); Statistical Mechanics (cond-mat.stat-mech)
Cite as: arXiv:2103.11041 [nlin.CD]
  (or arXiv:2103.11041v2 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.2103.11041
Journal reference: Chaos, Solitons & Fractals, 147 110954 (2021)
Related DOI: https://doi.org/10.1016/j.chaos.2021.110954

Submission history

From: Stefano Iubini [view email]
[v1] Fri, 19 Mar 2021 22:04:33 UTC (127 KB)
[v2] Tue, 11 May 2021 15:47:58 UTC (87 KB)
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