Abstract :
The study of imperfect Bose gases provides an opportunity to understand how irreversibility arises in superflows, as it is the unique dynamical model where hydrodynamics can be related in a rational way to microscopic dynamics. In the late 1950s I. Prigogine and P. Résibois (Superfluidité et équations de transport quantique, Monographie N6, Instituts Interuniversitaires des sciences nucléaires, Bruxelles, 1960) laid the foundations of such a kinetic theory. One difficulty in this endeavor is the coupling between the condensate and the normal gas, because this normal gas cannot be reduced to a system of quasi-particles dynamically independent of the condensate. It is proposed to investigate this question by extending the Bogoliubov theory, valid at equilibrium and without self-interaction of the normal gas, to situations out of equilibrium and with a finite proportion of particles in the normal state. One must see the resulting theory as an expansion of the collision operator in powers of the strength of the interaction. The lowest (or Vlasov, or Bogoliubov) order, the only one considered here, is already highly nontrivial and shows an unexpected feature, the exchange of mass, energy and momentum between the normal and condensed part of the gas in nonequilibrium situations. The structure of the term of mass exchange shows that, besides uniform flows and superfluid vortices, there is no stationary superflow without normal flow. Although this kind of phenomenon has long been known to be possible, it has a far more complex mathematical representation than anticipated long ago by C.J. Gorter and C.H. Mellink [Physica 15 (1949) 285]. It might be a basis for explaining that superfluidity breaks at velocities far below the critical Landau velocity.
