Hydrodynamic Lyapunov Modes in Translation Invariant Systems

Details Hydrodynamic Lyapunov Modes in Translation Invariant Systems Hydrodynamic Lyapunov Modes in Translation Invariant Systems

1999-08-18

arxiv.org/abs/chao-dyn/9908018v1

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 23 pages, 4 figures

Scientific paper

We study the implications of 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, Ch., Posch, H.A., Hoover, W.G., Phys. Rev. E 53, 1485 (1996)]. The hydrodynamic Lyapunov vectors loose 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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