Journal of Statistical Physics

, Volume 109, Issue 3–4, pp 765–776 | Cite as

Lyapunov Modes of Two-Dimensional Many-Body Systems; Soft Disks, Hard Disks, and Rotors

  • Wm. G. Hoover
  • Harald A. Posch
  • Christina Forster
  • Christoph Dellago
  • Mary Zhou


The dynamical instability of many-body systems can best be characterized through the local Lyapunov spectrum {λ}, its associated eigenvectors {δ}, and the time-averaged spectrum {〈λ〉}. Each local Lyapunov exponent λ describes the degree of instability associated with a well-defined direction—given by the associated unit vector δ—in the full many-body phase space. For a variety of hard-particle systems it is by now well-established that several of the δ vectors, all with relatively-small values of the time-averaged exponent 〈λ〉, correspond to quite well-defined long-wavelength “modes.” We investigate soft particles from the same viewpoint here, and find no convincing evidence for corresponding modes. The situation is similar—no firm evidence for modes—in a simple two-dimensional lattice-rotor model. We believe that these differences are related to the form of the time-averaged Lyapunov spectrum near 〈λ〉=0.

Local Lyapunov exponents Lyapunov modes hard disk fluid soft disk fluid 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Wm. G. Hoover
    • 1
    • 5
  • Harald A. Posch
    • 2
  • Christina Forster
    • 2
  • Christoph Dellago
    • 3
  • Mary Zhou
    • 4
  1. 1.Department of Applied ScienceUniversity of CaliforniaDavis/Livermore
  2. 2.awrence Livermore National LaboratoryLivermore
  3. 3.Institute for Experimental PhysicsUniversity of ViennaViennaAustria
  4. 4.Department of ChemistryUniversity of RochesterRochester
  5. 5.University of California at DavisDavis

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