Chaos and localization in the Discrete Nonlinear Schrödinger Equation

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.

arXiv comment7 pages, 7 figures

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Cited by in corpus (11)

• Lyapunov spectrum scaling for classical many-body dynamics close to integrability
• Thermalization slowing down in multidimensional Josephson junction networks
• Heat transport in long-ranged anharmonic oscillator models
• Quantum-classical correspondence of strongly chaotic many-body spin models
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Intensity pseudo-localized phase in the glassy random laser
• Deconfinement of classical Yang-Mills color fields in a disorder potential
• Frozen dynamics of a breather induced by an adiabatic invariant
• Trotter transition in BCS pairing dynamics
• Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization