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Related Experiment Videos

Nonhyperbolic behavior in the thermostated Lorentz gas.

H Odbadrakh1, G P Morriss

  • 1School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

Nonhyperbolic behavior in random Lorentz gas periodic orbits appears above field strength one. Further analysis reveals three orbit classes, including complex dynamics within the nonergodic elliptic region.

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Area of Science:

  • Statistical mechanics
  • Dynamical systems theory
  • Chaos theory

Background:

  • The behavior of particles in random Lorentz gases is crucial for understanding transport phenomena.
  • Periodic orbits play a key role in characterizing the dynamics of complex systems.
  • Thermostating and pruning are essential techniques for studying these systems.

Purpose of the Study:

  • To investigate the conditions for nonhyperbolic behavior in length-2 periodic orbits of the thermostated random Lorentz gas.
  • To classify the different types of period-2 orbits and their stability properties.
  • To explore the complex dynamics within the nonergodic elliptic region.

Main Methods:

  • Analysis of length-2 periodic orbits in a thermostated random Lorentz gas model.

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  • Stability analysis to classify orbits into elliptic and hyperbolic types.
  • Detailed dynamical study focusing on the nonhyperbolic region.

    • Main Results:

    • Nonhyperbolic behavior is observed only at field strengths greater than unity.
    • The range of fields for nonhyperbolic behavior is reduced in the pruned thermostatted periodic Lorentz gas.
    • Three classes of period-2 orbits were identified: elliptic and two distinct hyperbolic types.
    • Trajectories in the nonergodic elliptic region exhibit complex behavior analogous to perturbed resonant tori.

    Conclusions:

    • The study precisely defines the field strength threshold for nonhyperbolic dynamics in this system.
    • The classification of orbits provides a deeper understanding of the system's stability and behavior.
    • The observed complex dynamics in the elliptic region warrant further investigation within the context of Hamiltonian systems.