Dispersion of particles in an infinite-horizon Lorentz gas

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

doi:10.1103/PhysRevE.98.010101

Dispersion of particles in an infinite-horizon Lorentz gas

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

Department of Physics

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12 Scopus citations

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→, 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 language	English
Article number	010101
Journal	Physical Review E
Volume	98
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevE.98.010101
State	Published - 10 Jul 2018

Bibliographical note

Publisher Copyright:
© 2018 American Physical Society.

Funding

Acknowledgments. This work was supported by the Israel Science Foundation Grant No. 1898/17 (L.Z., I.F., and E.B.). Numerical simulations were supported by the Russian Science Foundation Grant No. 16-12-10496 (S.D.).

Funders	Funder number
Israel Science Foundation	1898/17
Russian Science Foundation	16-12-10496

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10.1103/PhysRevE.98.010101

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Dispersion of particles in an infinite-horizon Lorentz gas

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