Dispersion of particles in an infinite-horizon Lorentz gas

Lior Zarfaty, Alexander Peletskyi, Itzhak Fouxon, Sergey Denisov, Eli Barkai

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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→, 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.

Original languageEnglish
Article number010101
JournalPhysical Review E
Issue number1
StatePublished - 10 Jul 2018

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© 2018 American Physical Society.


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