Chaotic distributions for relativistic particles

Dawan  Mustafa; Bernt  Wennberg

doi:10.3934/krm.2016014

Article Contents

2016, Volume 9, Issue 4: 749-766. Doi: 10.3934/krm.2016014

This issue Previous Article Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos Next Article Global existence for the 2D Navier-Stokes flow in the exterior of a moving or rotating obstacle

Chaotic distributions for relativistic particles

Dawan Mustafa^1, and
Bernt Wennberg^1,

1.
Department of Mathematical sciences, Chalmers University of Technology and the University of Gothenburg, 412 96 GÖTEBORG

Received: June 30, 2015

Revised: March 31, 2016

Published: November 2016

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Abstract

We study a modified Kac model where the classical kinetic energy is replaced by an arbitrary energy function $\phi(v)$, $v \in \mathbb{R}$. The aim of this paper is to show that the uniform density with respect to the microcanonical measure is $Ce^{-z_0\phi(v)}$-chaotic, $C,z_0 \in \mathbb{R}_+$. The kinetic energy for relativistic particles is a special case. A generalization to the case $v\in \mathbb{R}^d$ which involves conservation momentum is also formally discussed.

Keywords:

Mathematics Subject Classification: Primary: 60K35, 82B40, 82C40; Secondary: 60J75, 83A05.

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