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Fermi-Pasta-Ulam phenomenon for generic initial data.

A Carati1, L Galgani, A Giorgilli

  • 1Department of Mathematics, University of Milano, Via Saldini 50, I-20133 Milano, Italy. carati@mat.unimi.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
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The Fermi-Pasta-Ulam (FPU) model exhibits a lack of energy equipartition at low energies, indicating a non-mixing property. Numerical simulations support this, showing persistent non-mixing behavior even in the thermodynamic limit.

Area of Science:

  • * Physics
  • * Nonlinear dynamics
  • * Statistical mechanics

Background:

  • * The Fermi-Pasta-Ulam (FPU) phenomenon describes the failure of energy equipartition in certain dynamical systems.
  • * This suggests that the FPU model may lack the mixing property, crucial for statistical mechanics.
  • * Understanding this property is key to comprehending energy distribution in nonlinear systems.

Purpose of the Study:

  • * To provide numerical evidence for the non-mixing property of the FPU model at low energies.
  • * To investigate whether this non-mixing behavior persists in the thermodynamic limit.
  • * To analyze the decay of mode energy autocorrelations as an indicator of mixing.

Main Methods:

  • * Numerical computation of orbits for the FPU model.

Related Experiment Videos

  • * Sampling initial data from the microcanonical ensemble using Monte Carlo techniques.
  • * Analyzing the decay of autocorrelations of mode energies.

    • Main Results:

    • * Numerical indications suggest the FPU model does not exhibit mixing at low energies.
    • * High-frequency modes show autocorrelations tending towards positive values, not decay.
    • * Evidence points to the survival of this non-mixing property in the thermodynamic limit.

    Conclusions:

    • * The FPU model demonstrates a lack of mixing at low energies, contrary to typical assumptions.
    • * The observed non-mixing behavior is robust and appears to persist at thermodynamic scales.
    • * Whether mixing occurs in the long-time limit remains an open question.