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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Normal diffusion in crystal structures and higher-dimensional billiard models with gaps.

David P Sanders1

  • 1Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F., 04510 Mexico. dps@fciencias.unam.mx

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

Three-dimensional periodic Lorentz gases often show normal diffusion, even with large gaps allowing collision-free travel. This occurs when these infinite-horizon gaps are not excessively large, as demonstrated by simulations and higher-dimensional models.

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Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Dynamical systems

Background:

  • Periodic Lorentz gases involve particles scattering off crystalline arrays.
  • Understanding diffusion in systems with infinite horizons is crucial.
  • Previous studies often assumed finite horizons or restricted particle movement.

Purpose of the Study:

  • To investigate the diffusion behavior in three-dimensional periodic Lorentz gases.
  • To determine conditions under which normal diffusion occurs despite infinite horizons.
  • To explore the influence of gap size on diffusive properties.

Main Methods:

  • Heuristic analysis of particle trajectories.
  • Numerical simulations of a 3D Lorentz gas model.
  • Extension of findings to higher-dimensional billiard models.

Main Results:

  • Three-dimensional periodic Lorentz gases frequently exhibit normal diffusion.
  • Normal diffusion persists even with infinite horizons (collision-free paths).
  • The occurrence of normal diffusion depends on the dimension of the gaps, not just their existence.

Conclusions:

  • The presence of large, collision-free channels does not necessarily preclude normal diffusion in these systems.
  • The dimensionality of the gaps is a critical factor in determining diffusive regimes.
  • Findings are consistent across 3D models and higher-dimensional extensions.