Chaos and localization in the Discrete Nonlinear Schrödinger Equation

Stefano Iubini* (Corresponding Author), Antonio Politi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Article number110954
Number of pages6
JournalChaos, Solitons and Fractals
Early online date10 May 2021
DOIs
Publication statusE-pub ahead of print - 10 May 2021

Keywords

  • Discrete Nonlinear Schr ̈odinger Equation
  • Discrete breathers
  • Lyapunov spectrum
  • Lyapunov covariant vectors

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