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.

我们分析了一维离散非线性Schrödinger方程的混沌动力学。这种不可积分的模型在物理学的几个领域中普遍存在，描述了具有局部非线性势的耦合复振子阵列的行为。我们探索了不同能量密度值的Lyapunov谱，发现在无限温度下达到了Kolmogorov-Sinai熵的最大值。此外，我们重新讨论了松弛的动态冻结，使其达到平衡，这是在大型局部状态（离散呼吸）叠加到通用有限温度背景时发生的。我们表明，局部激发会诱发许多非常小但不消失的Lyapunov指数，这表明存在极长的特征时标。