The Boltzmann-Grad limit of the periodic Lorentz gas

J Marklof; A Strombergsson

doi:10.4007/annals.2011.174.1.7

The Boltzmann-Grad limit of the periodic Lorentz gas

J Marklof, A Strombergsson

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit). A generic path of the limiting process is a piecewise linear curve whose consecutive segments are generated by a Markov process with memory two.

Translated title of the contribution	The Botzmann-Grad limit of the periodic Lorentz gas
Original language	English
Pages (from-to)	225 - 298
Number of pages	64
Journal	Annals of Mathematics
Volume	174
Issue number	1
DOIs	https://doi.org/10.4007/annals.2011.174.1.7
Publication status	Published - Jan 2011

Bibliographical note

Publisher: Princeton University

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10.4007/annals.2011.174.1.7

http://annals.math.princeton.edu/2011/174-1/p07

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LONG TIME LIMIT OF CHAOTIC QUANTUNM DYNAMICS
Marklof, J. (Principal Investigator)
1/04/05 → 1/04/08
Project: Research

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abstract = "We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit). A generic path of the limiting process is a piecewise linear curve whose consecutive segments are generated by a Markov process with memory two.",

author = "J Marklof and A Strombergsson",

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AB - We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit). A generic path of the limiting process is a piecewise linear curve whose consecutive segments are generated by a Markov process with memory two.

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DO - 10.4007/annals.2011.174.1.7

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SP - 225

EP - 298

JO - Annals of Mathematics

JF - Annals of Mathematics

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The Boltzmann-Grad limit of the periodic Lorentz gas

Abstract

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