The low-density limit of the Lorentz gas: periodic, aperiodic and random
From MaRDI portal
Publication:5371314
zbMATH Open1373.82065arXiv1404.3293MaRDI QIDQ5371314
Author name not available (Why is that?)
Publication date: 25 October 2017
Abstract: The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical scatterers. More than one hundred years after its conception, it is still a major challenge to understand the nature of the kinetic transport equation that governs the macroscopic particle dynamics in the limit of low scatterer density (the Boltzmann-Grad limit). Lorentz suggested that this equation should be the linear Boltzmann equation. This was confirmed in three celebrated papers by Gallavotti, Spohn, and Boldrighini, Bunimovich and Sinai, under the assumption that the distribution of scatterers is sufficiently disordered. In the case of strongly correlated scatterer configurations (such as crystals or quasicrystals), we now understand why the linear Boltzmann equation fails and what to substitute it with. A particularly striking feature of the periodic Lorentz gas is a heavy tail for the distribution of free path lengths, with a diverging second moment, and superdiffusive transport in the limit of large times.
Full work available at URL: https://arxiv.org/abs/1404.3293
No records found.
No records found.
This page was built for publication: The low-density limit of the Lorentz gas: periodic, aperiodic and random
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5371314)
