Comptes Rendus
The generalized-kinetics-based equilibrium distribution function for composite particles
Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 461-467.

This work is devoted to the equilibrium distribution function for a fluid of mutually non-interacting identical composite point particles in three-dimensional physical space. The distribution function is derived within the generalized-kinetics (GK) vision from the proposed probabilistic model based on quantum-mechanical bosons and fermions. The first GK advantage is that the derivation does not involve any assumption on the interpolation between bosons and fermions whereas the resulting function provides this interpolation. The second GK advantage is that composons, the particles described with the GK-based distribution function, are considerably less schematic and more consistent physically than quons. Composons correspond to a specific case of Isakov's general q-commutation relation involving an infinite number of the q-coefficients. Connection of the composon concept to previous results in the literature is pointed out. A few directions for future research on the topic are formulated. The results of the work can be used in the composite-particle fluid problems where the Maxwell–Boltzmann description is not valid, for instance, in dense populations of not too massive point-like particles of a complex, composite nature at not too high temperatures.

Ce travail s'intéresse à la fonction de distribution d'équilibre pour un fluide mutuellement non agissant, composé de particules points dans un espace de dimension trois. La fonction de distribution provient, d'un point de vue de CG, d'un modèle probabiliste issu de la mécanique quantique des fermions et des bosons. Le premier avantage de CG est que la dérivation ne nécessite aucune hypothèse sur l'interpolation entre les bosons et les fermions alors que la fonction résultante fournit cette interpolation. Le second est que les composons, les particules décrites par ce procédé sont considérablement moins schématiques et plus consistantes, physiquement, que les quons. Les composons correspondent à un cas particulier de la relation générale de q-commutation d'Isakov, pour un nombre infini de q-coefficients. Les résultats antérieurs liés au concept de composon sont signalés et quelques directions de recherches futures sont proposées. Les résultats de ce travail peuvent servir pour l'étude de fluides composés, où la description Maxwell–Boltzmann n'est pas valable, par exemple, pour une dense population de particules, pas trop lourdes et a des températures pas trop élevées, et d'une comoposition de nature complexe.

Published online:
DOI: 10.1016/S1631-0721(03)00111-6
Keywords: Fluid mechanics, quantum mechanics, Boson, Fermion, Distribution function, Composite particle, Generalized kinetics, q-commutation relation, Isakov's coefficient, Quon, Composon
Mot clés : Mécanique des fluides, mécanique quantique, Boson, Fermion, Fonction de distribution, Particules composées, Cinetique généralisée, Relation de q-commutation, Coefficients d'Isakov, Quon, Composon

Nicola Bellomo 1; Nils Calander 2; Eugen Mamontov 2; Magnus Willander 2

1 Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2 Laboratory of Physical Electronics and Photonics, School of Physics and Engineering Physics, Gothenburg University and Chalmers University of Technology, 412 96 Gothenburg, Sweden
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Nicola Bellomo; Nils Calander; Eugen Mamontov; Magnus Willander. The generalized-kinetics-based equilibrium distribution function for composite particles. Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 461-467. doi : 10.1016/S1631-0721(03)00111-6.

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