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Kinetic theory for the low-density Lorentz gas / Jens Marklof, Andreas Strömbergsson

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 294, number 1464 (February 2024)Publisher: Providence : American Mathematical Society, February 2024Description: v, 136 SeitenISBN:
  • 9781470468699
Subject(s): Additional physical formats: 9781470477219 | Erscheint auch als: Kinetic theory for the low-density Lorentz gas. Online-Ausgabe Providence, RI : American Mathematical Society, 2024. 1 Online-Ressource (v, 136 Seiten) | Erscheint auch als: Kinetic theory for the low-density Lorentz gas. Online-Ausgabe Providence : American Mathematical Society, 2024. 1 Online-Ressource (v, 136 Seiten)DDC classification:
  • 533.7
  • 533/.7 23/eng20240809
MSC: MSC: 82C40 | 60G55 | 35Q20 | 82C40RVK: RVK: SI 130LOC classification:
  • QC175.13
Summary: Keywords: Lorentz gas, Boltzmann-Grad limit, Boltzmann equation, random flight process, point process, quasicrystalSummary: The Lorentz gas is one of the simplest and most widely-studied models for particle transport in matter. It describes a cloud of non-interacting gas particles in an infinitely extended array of identical spherical scatterers. The model was introduced by Lorentz in 1905 who, following the pioneering ideas of Maxwell and Boltzmann, postulated that in the limit of low scatterer density, the macroscopic transport properties of the model should be governed by a linear Boltzmann equation. The linear Boltzmann equation has since proved a useful tool in the description of various phenomena, including semiconductor physics and radiative transfer. A rigorous derivation of the linear Boltzmann equation from the underlying particle dynamics was given, for random scatterer configurations, in three seminal papers by Gallavotti, Spohn and Boldrighini-Bunimovich-Sinai. The objective of the present study is to develop an approach for a large class of deterministic scatterer configurations, including various types of quasicrystals. We prove the convergence of the particle dynamics to transport processes that are in general (depending on the scatterer configuration) not described by the linear Boltzmann equation. This was previously understood only in the case of the periodic Lorentz gas through work of Caglioti-Golse and Marklof-Strömbergsson. Our results extend beyond the classical Lorentz gas with hard sphere scatterers, and in particular hold for general classes of spherically symmetric finite-range potentials. We employ a rescaling technique that randomises the point configuration given by the scatterers’ centers. The limiting transport process is then expressed in terms of a point process that arises as the limit of the randomised point configuration under a certain volume-preserving one-parameter linear group action.PPN: PPN: 1885387024
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c - 294.2024,1464 Nicht ausleihbar
Total holds: 0
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