[La fonction de distribution d'équilibre pour des particules composées basée sur la cinétique généralisée]
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.
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.
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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
@article{CRMECA_2003__331_7_461_0,
author = {Nicola Bellomo and Nils Calander and Eugen Mamontov and Magnus Willander},
title = {The generalized-kinetics-based equilibrium distribution function for composite particles},
journal = {Comptes Rendus. M\'ecanique},
pages = {461--467},
publisher = {Elsevier},
volume = {331},
number = {7},
year = {2003},
doi = {10.1016/S1631-0721(03)00111-6},
language = {en},
}
TY - JOUR AU - Nicola Bellomo AU - Nils Calander AU - Eugen Mamontov AU - Magnus Willander TI - The generalized-kinetics-based equilibrium distribution function for composite particles JO - Comptes Rendus. Mécanique PY - 2003 SP - 461 EP - 467 VL - 331 IS - 7 PB - Elsevier DO - 10.1016/S1631-0721(03)00111-6 LA - en ID - CRMECA_2003__331_7_461_0 ER -
%0 Journal Article %A Nicola Bellomo %A Nils Calander %A Eugen Mamontov %A Magnus Willander %T The generalized-kinetics-based equilibrium distribution function for composite particles %J Comptes Rendus. Mécanique %D 2003 %P 461-467 %V 331 %N 7 %I Elsevier %R 10.1016/S1631-0721(03)00111-6 %G en %F CRMECA_2003__331_7_461_0
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. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00111-6/
[1] Statistical Physics, Part 1, Pergamon Press, Oxford, 1980
[2] Experimental verification of the Heisenberg uncertainty principle for fullerence molecules, Phys. Rev. A, Volume 65 (2002), p. 032109/1-032109/4
[3] Intermediate Quantum Mechanics, Benjamin–Cummings, Menlo Park, 1986
[4] Notes on the statistics of nuclei, Phys. Rev., Volume 37 (1931) no. 4, pp. 333-338
[5] Generalization of quantum statistics in statistical mechanics, Int. J. Theor. Phys., Volume 32 (1993) no. 5, pp. 737-767
[6] Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models, World Scientific, Singapore, 2000
[7] Generalized kinetic (Boltzmann) models: Mathematical structures and applications, Math. Models Methods Appl. Sci., Volume 12 (2002) no. 4, pp. 567-591
[8] N. Bellomo, E. Mamontov, M. Willander, On the generalized kinetic modelling of a multicomponent “real-life” fluid by means of a single distribution function, Math. Comput. Modelling (2003) 21 pp., accepted
[9] Theory of Quanta, Oxford University Press, New York–Oxford, 1992
[10] Spin in Particle Physics, Cambridge University Press, Cambridge, 2001
[11] Example of infinite statistics, Phys. Rev. Lett., Volume 64 (1990) no. 7, pp. 705-708
[12] Particles with small violations of Fermi or Bose statistics, Phys. Rev. D, Volume 43 (1991) no. 12, pp. 4111-4120
[13] “Fractional statistics” in arbitrary dimensions: a generalization of the Pauli principle, Phys. Rev. Lett., Volume 67 (1991) no. 8, pp. 937-940
[14] Generalization of statistics for several species of identical particles, Mod. Phys. Lett. B, Volume 8 (1994) no. 5, pp. 319-327
[15] Statistical distribution for generalized ideal gas of fractional-statistics particles, Phys. Rev. Lett., Volume 73 (1994) no. 7, pp. 922-925
[16] Spin dependence of the thermal neutron cross section of Ho165, Phys. Rev., Volume 136 (1964) no. 5B, p. B1285-B1288
[17] Measurement of the average circular γ-polarization and determination of spins for compound states formed in thermal neutron capture, Nucl. Phys. A, Volume 147 (1970) no. 1, pp. 150-160
[18] Scattering of charge carriers on a high spin-low spin mixture in MnAs1−xPx crystals, Phys. Lett. A, Volume 91 (1982) no. 7, pp. 361-364
[19] Gravitational waves from solar oscillations: Proposal for a transition-zone test of general relativity, Class. Quantum Grav., Volume 2 (1985) no. 3, pp. 381-402
[20] Ferrihemoprotein hydroxides: a correlation between magnetic and spectroscopic properties, Rev. Mod. Phys., Volume 36 (1964) no. 1, pp. 441-458
[21] Spin state and axial ligand bonding in the hydroxide complexes of metmyoglobin, methemoglobin, and horseradish peroxidase at room and low temperatures, Biochemistry, Volume 33 (1994) no. 15, pp. 4577-4583
[22] Spin–spin interactions in the reduced [Fe6S6]5+ cluster, Chem. Phys., Volume 213 (1–3) (1996), pp. 45-62
[23] Onset of Fermi degeneracy in a trapped atomic gas, Science, Volume 285 (1999), pp. 1703-1706
[24] Pauli blocking of collisions in a quantum degenerate atomic Fermi gas, Phys. Rev. Lett., Volume 86 (2001) no. 24, pp. 5409-5412
[25] Tables of Integrals and Other Mathematical Data, Macmillan, New York, 1961
[26] The canonical partition function for quons, Phys. Lett. A, Volume 195 (1994) no. 1, pp. 38-42
[27] Quon gas with the boson, fermion, and near-classical limits, Phys. Rev. A, Volume 52 (1995) no. 2, pp. 932-935
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