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 language | English |
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Article number | 110954 |
Number of pages | 6 |
Journal | Chaos, Solitons and Fractals |
Early online date | 10 May 2021 |
DOIs | |
Publication status | Published - 30 Jun 2021 |
Keywords
- Discrete Nonlinear Schr ̈odinger Equation
- Discrete breathers
- Lyapunov spectrum
- Lyapunov covariant vectors