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Kraemer AS, Schmiedeberg M, Sanders DP. Horizons and free-path distributions in quasiperiodic Lorentz gases. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;92(5):052131doi: 10.1103/PhysRevE.92.052131.
Kraemer, A. S., Schmiedeberg, M., & Sanders, D. P. (2015). Horizons and free-path distributions in quasiperiodic Lorentz gases. Physical review. E, Statistical, nonlinear, and soft matter physics, 92(5), 052131. https://doi.org/10.1103/PhysRevE.92.052131
Kraemer, Atahualpa S, et al. "Horizons and free-path distributions in quasiperiodic Lorentz gases." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 92,5 (2015): 052131. doi: https://doi.org/10.1103/PhysRevE.92.052131
Kraemer AS, Schmiedeberg M, Sanders DP. Horizons and free-path distributions in quasiperiodic Lorentz gases. Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Nov;92(5):052131. doi: 10.1103/PhysRevE.92.052131. Epub 2015 Nov 20. PMID: 26651670.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Nov;92(5):052131. doi: 10.1103/PhysRevE.92.052131. Epub 2015 Nov 20.

Horizons and free-path distributions in quasiperiodic Lorentz gases.

Physical review. E, Statistical, nonlinear, and soft matter physics

Atahualpa S Kraemer, Michael Schmiedeberg, David P Sanders

Affiliations

  1. Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.
  2. Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510, Mexico.

PMID: 26651670 DOI: 10.1103/PhysRevE.92.052131

Abstract

We study the structure of quasiperiodic Lorentz gases, i.e., particles bouncing elastically off fixed obstacles arranged in quasiperiodic lattices. By employing a construction to embed such structures into a higher-dimensional periodic hyperlattice, we give a simple and efficient algorithm for numerical simulation of the dynamics of these systems. This same construction shows that quasiperiodic Lorentz gases generically exhibit a regime with infinite horizon, that is, empty channels through which the particles move without colliding, when the obstacles are small enough; in this case, the distribution of free paths is asymptotically a power law with exponent -3, as expected from infinite-horizon periodic Lorentz gases. For the critical radius at which these channels disappear, however, a new regime with locally finite horizon arises, where this distribution has an unexpected exponent of -5, previously observed only in a Lorentz gas formed by superposing three incommensurable periodic lattices in the Boltzmann-Grad limit where the radius of the obstacles tends to zero.

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