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The anti-FPU problem.

Thierry Dauxois1, Ramaz Khomeriki, Francesco Piazza

  • 1Laboratoire de Physique, UMR-CNRS 5672, ENS Lyon, 46 Allée d'Italie, 69364 Lyon Cédex 07, France.

Chaos (Woodbury, N.Y.)
|April 20, 2005
PubMed
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The Anti-FPU problem describes energy transfer to high frequencies in Fermi-Pasta-Ulam (FPU) lattices, forming chaotic breathers. Systems relax to equipartition, with longer relaxation times at lower energy densities.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • The Fermi-Pasta-Ulam (FPU) problem investigates energy flow in nonlinear lattices.
  • Modulational instability is a key phenomenon in nonlinear systems.

Purpose of the Study:

  • To analyze the modulational instability of the zone-boundary mode in FPU lattices.
  • To investigate the subsequent relaxation dynamics and formation of chaotic breathers.

Main Methods:

  • Detailed numerical analysis of one and higher-dimensional FPU lattices.
  • Examination of energy flow and spectral properties.
  • Simulation of lattice cooling at edges.

Main Results:

  • Instability of the zone-boundary mode leads to the Anti-FPU problem, where energy initially flows to high frequencies.

Related Experiment Videos

  • Chaotic breathers are formed in both 1D and 2D FPU lattices.
  • System relaxation to energy equipartition occurs on time scales inversely dependent on energy density.

    • Conclusions:

    • The Anti-FPU problem provides a contrasting perspective to the original FPU problem.
    • Chaotic breathers exhibit qualitative similarities whether formed through Anti-FPU dynamics or lattice cooling.
    • Understanding these dynamics is crucial for nonlinear lattice behavior.