Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 98, Issue 3-4, Pages 775-798Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1018679609870
Keywords
nonlinear dynamics; Hamiltonian dynamics; extended systems; random matrices; Lyapunov spectrum; hydrodynamic modes
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We study the implications elf translation invariance on the tangent dynamics of extended dynamical systems, within a random matrix approximation. In a model system, we show the existence of hydrodynamic modes in the slowly growing part of the Lyapunov spectrum, which are analogous to the hydrodynamic modes discovered numerically by Dellago, Posch, and Hoover. The hydrodynamic Lyapunov vectors lose the typical random structure and exhibit instead the structure of weakly perturbed coherent long-wavelength waves. We show further that the amplitude of the perturbations vanishes in the thermodynamic limit, and that the associated Lyapunov exponents are universal.
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