A Kinetic Equation for Quantum Gases

Abstract : We apply the formalism of the free Wigner transform to the derivation of a kinetic equation valid for dilute quantum gases; this formalism is compatible with a precise treatment of two-body correlations and allows the inclusion of second virial corrections. We generalize the results obtained in previous articles where the calculation of the collision integral was limited to zero ("local") and first order gradient terms; here we use a more general ("non-local") form for the interaction term which is an integral of higher dimension (18). The conservation laws are studied in this formalism, which implies non-linear expressions for the local hydrodynamic quantities in terms of the function appearing in the kinetic equation. The pressure at thermal equilibrium is then evaluated and found to be equal to the value predicted by the Beth-Uhlenbeck formula, without adjusting any free parameter of the theory.
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Contributor : Geneviève Tastevin <>
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  • HAL Id : hal-02016721, version 1


Pierre-Jean Nacher, G. Tastevin, F. Laloë. A Kinetic Equation for Quantum Gases. Annalen der Physik, 1991, 48 (1-3), pp.149--168. ⟨hal-02016721⟩



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