Dispersion of particles in an infinite-horizon Lorentz gas

Abstract

We consider a two-dimensional Lorentz gas with infinite horizon. This paradigmatic model consists of pointlike particles undergoing elastic collisions with fixed scatterers arranged on a periodic lattice. It was rigorously shown that when $t\to \infty$, the distribution of particles is Gaussian. However, the convergence to this limit is ultraslow, hence it is practically unattainable. Here we obtain an analytical solution for the Lorentz gas' kinetics on physically relevant timescales, and find that the density in its far tails decays as a universal power law of exponent $-3$. We also show that the arrangement of scatterers is imprinted in the shape of the distribution.

Article with supplemental material: 10 pages, 4 figures

References in corpus (6)

• Power-law distributions in empirical data
• Lévy walks
• Splitting of the universality class of anomalous transport in crowded media
• Superdiffusive dispersals impart the geometry of underlying random walks
• Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
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Cited by in corpus (8)

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• Infinite horizon billiards: Transport at the border between Gauss and Lévy universality classes
• Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows
• Anomalous Diffusion in the Square Soft Lorentz Gas
• In the folds of the Central Limit Theorem: Lévy walks, large deviations and higher-order anomalous diffusion
• Asymptotic densities of planar Lévy walks: a non-isotropic case