The Boltzmann equation for Bose-Einstein particles: condensation in finite time
type: Item
instance of: scholarly article
title: The Boltzmann equation for Bose-Einstein particles: condensation in finite time
zbMATH Open document ID: 1277.82041
author: Xuguang Lu
published in: Journal of Statistical Physics
publication date: 2013-05-17T00:00:00Z
review text: The paper under review deals with the isotropic and spatially homogeneous Boltzmann equation for Bose-Einstein particles in the case of the hard sphere model, and tackles the problem of Bose-Einstein condensation in finite time. The main result states that if the initial energy distribution of particles has no mass at 0 but is singular enough near the origin, then condensation occurs at all positive times. In the first section, the author introduces the equation of interest, defines the notion of a distributional solution, recalls several results such as the existence of an equilibrium distributional solution and a critical temperature, as well as a result on the convergence to equilibrium, and finally raises the question of condensation in finite time. The latter is partially answered by the main theorem in Section 2, whereas Section 3 contains the proof. Implications of the result, in particular, the link between condensation and conservation of mass, are discussed in Section 4. In the appendix, it is proved that the definition of a distributional solution given in [\textit{X. Lu}, J. Stat. Phys. 116, No. 5--6, 1597--1649 (2004; Zbl 1097.82023)] is equivalent to the one in the present paper.
reviewed by: Julien Poisat
Mathematics Subject Classification ID: 82C26
Mathematics Subject Classification ID: 35Q20
Mathematics Subject Classification ID: 82B26
zbMATH DE Number: 6164077
zbMATH Keywords: Boltzmann equation
zbMATH Keywords: Bose-Einstein particles
zbMATH Keywords: hard sphere model
zbMATH Keywords: condensation
zbMATH Keywords: finite time
MaRDI profile type: Publication
full work available at URL: s10955-013-0725-9
OpenAlex ID: W2164357530
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DOI: 10.1007/S10955-013-0725-9
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description: scientific article; zbMATH DE number 6164077