Hydrodynamic Lyapunov modes in translation-invariant systems

Jean Pierre Eckmann*, Omri Gat

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


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.

Original languageAmerican English
Pages (from-to)775-798
Number of pages24
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Feb 2000
Externally publishedYes


  • Extended systems
  • Hamiltonian dynamics
  • Hydrodynamic modes
  • Lyapunov spectrum
  • Nonlinear dynamics
  • Random matrices


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