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Physica A Statistical Mechanics and its Applications

Statistical quasi-particles as the normal component of a superfluid

Richard Norton

Published May 1, 1989• 1 citation
Publisher
DOI
10.1016/0378-4371(89)90503-7

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This chapter considers the behavior of the superfluid Bose liquid at finite temperatures. The thermally-excited quasi-particles are identified with the normal fluid. In general, their motion will be irreversible and may be described, in suitable limit, with the aid of a coefficient of viscosity. Consideration of the rotating bucket experiment provides such a prescription, both experimentally and theoretically. Since condensate motion is irrotational, the superfluid component will not respond to rotation of its container. Collisions with the walls thus represent the physical mechanism by which the normal fluid is singled out, the superfluid component being unaffected by the presence of the pipe. According to the two-fluid model, the velocity of the normal fluid vanishes, since it is "attached" to the walls of the pipe by viscous effects. As a consequence of superfluid flow, the thermal quasi-particle distribution is asymmetric in momentum space.
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At finite temperature, the hydrodynamic collective modes of superfluid trapped Fermi gases are coupled to the motion of the normal component, which in the BCS limit behaves like a collisionless normal Fermi gas. The coupling between the superfluid and the normal components is treated in the framework of a semiclassical transport theory for the quasiparticle-distribution function, combined with a hydrodynamic equation for the collective motion of the superfluid component. We develop a numerical test-particle method for solving these equations in the linear-response regime. As a first application we study the temperature dependence of the collective quadrupole mode of a Fermi gas in a spherical trap. The coupling between the superfluid collective motion and the quasiparticles leads to a rather strong damping of the hydrodynamic mode already at very low temperatures. At higher temperatures the spectrum has a two-peak structure, the second peak corresponding to the quadrupole mode in the normal phase.