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Recurrence for quenched random Lorentz tubes.

Giampaolo Cristadoro1, Marco Lenci, Marcello Seri

  • 1Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy. cristadoro@dm.unibo.it

Chaos (Woodbury, N.Y.)
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This study examines billiard dynamics within a strip tiled by polygons, incorporating random scatterers. Researchers proved that these complex systems, known as quenched random Lorentz tubes, are generally recurrent.

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Area of Science:

  • Mathematical Physics
  • Dynamical Systems Theory
  • Statistical Mechanics

Background:

  • Billiard systems model particle motion in confined spaces.
  • Lorentz gas models explore transport properties in disordered systems.
  • Tessellated domains introduce complex geometric structures to dynamical systems.

Purpose of the Study:

  • To investigate the recurrence properties of billiard dynamics in a specific tessellated domain.
  • To analyze the behavior of a quenched random Lorentz tube model.
  • To establish conditions for recurrence in a system with random scatterers.

Main Methods:

  • Analysis of billiard trajectories within a strip tessellated by translated polygons.
  • Introduction of a random configuration of semidispersing scatterers.
  • Mathematical formulation and analysis of the quenched random Lorentz tube ensemble.

Main Results:

  • Demonstration that under general conditions, almost every system within the ensemble exhibits recurrent behavior.
  • Characterization of the statistical properties of the dynamical systems.
  • Proof of recurrence for a broad class of configurations.

Conclusions:

  • The study confirms the prevalence of recurrent dynamics in quenched random Lorentz tubes.
  • The findings contribute to the understanding of chaotic and statistical properties in disordered systems.
  • Recurrence is a general feature, not an exception, in this specific tessellated billiard model.