Abstract
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, 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
G. Paladin and A. Vulpiani, J. Phys. A 19:1881 (1986).
R. Livi, A. Politi, S. Ruffo, and A. Vulpiani, J. Stat. Phys. 46:197 (1987).
J.-P. Eckmann and C. E. Wayne, J. Stat. Phys. 50:853 (1988).
Ch. Dellago, H. A. Posch, and W. G. Hoover, Phys. Rev. E 53:1485 (1996).
H. A. Posch and R. Hirschl, Simulation of billiards and of hard-body fluids, preprint (1999).
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Fluctuations, Benjamin Cummings, London, (1983).
S. Lepri, R. Livi, and A. Politi, Europhys. Lett. 43:271 (1998).
A. Politi, private communication.
L. S. Young, Erg. Th. Dyn. Syst. 6:627 (1986).
M. H. Partovi, Phys. Rev. Lett. 82:3424 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eckmann, JP., Gat, O. Hydrodynamic Lyapunov Modes in Translation-Invariant Systems. Journal of Statistical Physics 98, 775–798 (2000). https://doi.org/10.1023/A:1018679609870
Issue Date:
DOI: https://doi.org/10.1023/A:1018679609870