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Diffusion in Hamiltonian systems.

V. V. Kozlov1, N. G. Moshchevitin

  • 1Faculty of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary

This study explores diffusion in degenerate Hamiltonian systems, finding that action variables can diffuse. For systems with three degrees of freedom, faster diffusion rates are achievable.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Degenerate Hamiltonian systems are complex dynamical systems.
  • Understanding diffusion in these systems is crucial for statistical mechanics.

Purpose of the Study:

  • To investigate the phenomenon of diffusion in a model of degenerate Hamiltonian systems.
  • To analyze the behavior of action variables during diffusion.

Main Methods:

  • The study considers a specific Hamiltonian: the sum of a linear function of action variables and a periodic function of angle variables.
  • Analysis is performed for systems with two and three degrees of freedom.

Main Results:

  • Diffusion of action variables is shown to exist under specific conditions.
  • In two-degree-of-freedom systems, action variables repeatedly return near their initial values during diffusion.
  • In three-degree-of-freedom systems, diffusion rates faster than any prescribed rate can be achieved.

Conclusions:

  • The model demonstrates the possibility of diffusion in degenerate Hamiltonian systems.
  • The number of degrees of freedom significantly influences diffusion behavior and achievable rates.

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