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Chaotic distributions for relativistic particles

Journal article
Authors Dawan Mustafa
Bernt Wennberg
Published in Kinetic and Related Models
Volume 9
Issue 4
Pages 749-766
ISSN 1937-5093
Publication year 2016
Published at Department of Mathematical Sciences, Mathematics
Pages 749-766
Language en
Links dx.doi.org/10.3934/krm.2016014
Keywords Chaotic distributions, Master equation, Microcanonical measure, Propagation of chaos, Relativistic Kac model
Subject categories Mathematics

Abstract

© American Institute of Mathematical Sciences.We study a modified Kac model where the classical kinetic energy is replaced by an arbitrary energy function φ(v), v ∈ ℝ. The aim of this paper is to show that the uniform density with respect to the microcanonical measure is Ce-z0φ(v)-chaotic, C, z0 ∈ ℝ+. The kinetic energy for relativistic particles is a special case. A generalization to the case v ∈ ℝd which involves conservation momentum is also formally discussed.

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