Normal diffusion in crystal structures and higher-dimensional billiard models with gaps

Abstract

We show, both heuristically and numerically, that three-dimensional periodic Lorentz gases -- clouds of particles scattering off crystalline arrays of hard spheres -- often exhibit normal diffusion, even when there are gaps through which particles can travel without ever colliding, i.e., when the system has an infinite horizon. This is the case provided that these gaps are not "too big", as measured by their dimension. The results are illustrated with simulations of a simple three-dimensional model having different types of diffusive regime, and are then extended to higher-dimensional billiard models, which include hard-sphere fluids.

4 pages, 3 figures. v2: Minor revisions, references added

References in corpus (5)

• On the strong anomalous diffusion
• Occurrence of normal and anomalous diffusion in polygonal billiard channels
• Anomalous Diffusion in Infinite Horizon Billiards
• The existence of Burnett coefficients in the periodic Lorentz gas
• Fine structure of distributions and central limit theorem in diffusive billiards

Cited by in corpus (7)

• New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis
• Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
• Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases
• Tail asymptotics of free path lengths for the periodic Lorentz process. On Dettmann's geometric conjectures
• Horizons and free path distributions in quasiperiodic Lorentz gases
• Evolution of collision numbers for a chaotic gas dynamics
• Efficient algorithms for general periodic Lorentz gases in two and three dimensions