Chaos and localization in the discrete nonlinear Schrodinger equation

We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schrodinger equation. This non-integrable 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. (C) 2021 Elsevier Ltd. All rights reserved.