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Transport in the barrier billiard.

S M Saberi Fathi1, W Ettoumi2, M Courbage3

  • 1Department of Physics, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran.

Physical Review. E
|July 15, 2016
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Summary
This summary is machine-generated.

Transport properties of particles in a periodic barrier billiard depend heavily on the incidence angle. For fixed angles, motion is bounded or ballistic; for ensembles, anomalous diffusion emerges but decomposes into simpler subdynamics.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Investigating particle transport in complex systems is crucial for understanding phenomena from molecular dynamics to macroscopic fluid flow.
  • Periodic barrier systems present unique challenges due to their intricate phase space and potential for non-trivial dynamics.

Purpose of the Study:

  • To analyze the transport properties of particles within an infinite periodic horizontal planar barrier billiard.
  • To explore how the incidence angle (α) influences particle displacement and diffusion rates.
  • To characterize the behavior of particle ensembles with varying incidence angles.

Main Methods:

  • Theoretical analysis of particle trajectories and reflections within the billiard system.
  • Numerical computation to examine the second moment of displacement 〈S_{n}^{2}〉 over time (n).
  • Investigation of autocorrelation functions and ergodicity for different incidence angle behaviors.

Main Results:

  • For rational incidence angles (α), particle displacement is bounded or ballistic (asymptotic to Kn²).
  • For irrational α, transport is non-ballistic, with time-averaged autocorrelation decay, but not always for all irrational α.
  • Numerical results reveal superdiffusive, subdiffusive, or bounded transport depending on α, mirroring conservative system behaviors.

Conclusions:

  • Particle transport in this billiard system exhibits rich and angle-dependent behavior, including anomalous diffusion for ensembles.
  • Ensemble dynamics, initially non-ergodic, decompose into ergodic subdynamics, breaking self-similarity.
  • The study highlights the complex interplay between system geometry, incidence angle, and emergent transport phenomena.