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Related Experiment Videos

The nonequilibrium Lorentz gas.

James Lloyd1, Matthias Niemeyer, Lamberto Rondoni

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

Chaos (Woodbury, N.Y.)
|September 1, 1995
PubMed
Summary
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This study explores Lorentz gas conductivity under external fields. Researchers found that small fields maintain ergodicity, allowing accurate calculations, while large fields lead to complex dynamics and potential ergodicity breakdown.

Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • Investigates the conductivity of a Lorentz gas system, a model comprising fixed scatterers and a moving point particle.
  • Examines the system's behavior under an applied external field to achieve a nonequilibrium stationary state.
  • Utilizes a Gaussian thermostat to fix the particle's speed.

Purpose of the Study:

  • To analyze the conductivity of a Lorentz gas system as a function of external field strength.
  • To explore the impact of field strength on system dynamics, ergodicity, and thermodynamic variables.
  • To investigate the influence of scatterer array orientation on system behavior.

Main Methods:

  • Application of a Gaussian thermostat to maintain a nonequilibrium stationary state.

Related Experiment Videos

  • Utilizing the Periodic Orbit Expansion for calculating thermodynamic variables in the ergodic regime.
  • Detailed dynamical study of bifurcation sequences and transitions.

    • Main Results:

    • For small fields, the system exhibits ergodic behavior, and the diffusion coefficient is well-defined, validating the Periodic Orbit Expansion.
    • At larger field strengths, diverse dynamics emerge, including the breakdown of ergodicity and the emergence of a single stable trajectory.
    • System behavior is sensitive to the orientation of scatterers relative to the external field.

    Conclusions:

    • The study demonstrates the applicability of the Periodic Orbit Expansion for small fields in Lorentz gases.
    • Highlights the complex dynamical transitions and potential ergodicity loss in Lorentz gases under strong external fields.
    • Provides insights into the relationship between external fields, system dynamics, and ergodicity in statistical mechanics models.