Dynamique des gaz quantiques (particules discernables sans spin)

نویسندگان

  • Geneviève Tastevin
  • Pierre-Jean Nacher
  • Franck Laloë
چکیده

Nous appliquons les résultats de deux articles précédents, en particulier uné equation cinétique généralisant l'´ equation de Boltzmann, ` a l'´ etude des gaz dilués quantiques hors d'´ equilibre. Par une simple extension de la méthode de Chapman Enskog appliquéè a cetté equation cinétique, nous calculons les propriétés hydrodynamiques du gaz. A l'ordre le plus bas (hydrodynamique d'Euler), nous obtenons des résultats pour la pression, la vitesse du son et la capacité calorifique qui, contrairementà ceux de la théorie de Boltzmann, contiennent les secondes corrections du viriel. A l'ordre suivant (hydrodynamique visqueuse, ou de Navier Stokes), nous obtenons les corrections du premier ordre en densité aux coefficients de transport, et montrons qu'il peut exister un terme de seconde viscosité, quadratique en densité. Ce formalisme donne accès aux parties des corrections du viriel des coefficients de transport qui dépendent des collisionsà deux corps, mais pasà celles qui sont dues aux collisions ternaires. Il est quantique et permet de réobtenir l'expression de Beth et Uhlenbeck de la seconde correction du viriel en fonction des déphasages. Abstract: We apply the results obtained in two preceding articles, in particular a kinetic equation which generalizes the Boltzmann equation, to the study of dilute quantum gases out of equilibrium. Extending the Chapman Enskog method to this equation, and taking into account the specific expressions of the locally conserved quantities in this theory, we calculate the hydrodynamical properties of the gas. To lowest order (Euler hydrodynamics), we obtain results which include second virial corrections to the pressure, sound velocity and specific heat, which are not accessible within the usual frame of the the Boltzmann equation. To first order (viscous , or Navier Stokes, hydrodynamics), we get linear density corrections to transport coefficients. We also show that bulk viscosity may exist, being proportional to the square of density. This formalism gives access to the part of the second virial corrections to transport coefficients which correspond to transport by binary collisions, but ignores the modifications of the damping of currents due to three body interactions (although it does provide virial corrections to the damping of non hydrodynamical variables). It is purely quantum and, at equilibrium, allows one to recover the Beth Uhlenbeck expression of the second virial correction to the pressure in terms of the collision phase shifts. It will be extended to spin and statistics in a forthcoming article.

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تاریخ انتشار 2016