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Journal of Statistical Physics

, Volume 172, Issue 3, pp 762–780 | Cite as

Equilibration and Diffusion for a Dynamical Lorentz Gas

  • Émilie Soret
Article
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Abstract

We consider a model of a dynamical Lorentz gaz: a single particle is moving in \({\mathbb {R}}^d\) through an array of fixed and soft scatterers each possessing an internal degree of freedom coupled to the particle. Assuming the initial velocity is sufficiently high and modelling the parameters of the scatterers as random variables, we describe the evolution of the kinetic energy of the particle by a Markov chain for which each step corresponds to a collision. We show that the momentum distribution of the particle approaches a Maxwell–Boltzmann distribution with effective temperature T such that \(k_BT\) corresponds to an average of the scatterers’ kinetic energy.

Keywords

Mathematical physics Probability Lorentz gas Diffusion processes Equilibration Stationary distribution 

Notes

Acknowledgements

This work is in part supported by IRCICA, USR CNRS 3380 and the Labex CEMPI (ANR-11- LABX-0007-01). The author thanks S. De Bièvre and P.E. Parris for their helpful discussions.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IEMN UMR CNRS 8520Villeneuve-d’AscqFrance
  2. 2.IRCICA CNRS 3024Villeneuve-d’AscqFrance

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