Collective modes of trapped Fermi gases with in-medium interaction

Due to Pauli blocking of intermediate states, the scattering matrix (or $T$ matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium $T$ matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.Comment: 17 page

Two-fluid model for a rotating trapped Fermi gas in the BCS phase

We investigate the dynamical properties of a superfluid gas of trapped fermionic atoms in the BCS phase. As a simple example we consider the reaction of the gas to a slow rotation of the trap. It is shown that the currents generated by the rotation can be understood within a two-fluid model similar to the one used in the theory of superconductors, but with a position dependent ratio of normal and superfluid densities. The rather general result of this paper is that already at very low temperatures, far below the critical one, an important normal-fluid component appears in the outer regions of the gas. This renders the experimental observation of superfluidity effects more difficult and indicates that reliable theoretical predictions concerning other dynamical properties, like the frequencies of collective modes, can only be made by taking into account temperature effects.Comment: 6 pages, 4 figure

Averaged null energy condition violation in a conformally flat spacetime

We show that the averaged null energy condition can be violated by a conformally coupled scalar field in a conformally flat spacetime in 3+1 dimensions. The violation is dependent on the quantum state and can be made as large as desired. It does not arise from the presence of anomalies, although anomalous violations are also possible. Since all geodesics in conformally flat spacetimes are achronal, the achronal averaged null energy condition is likewise violated.Comment: 11 page

Coupling of hydrodynamics and quasiparticle motion in collective modes of superfluid trapped Fermi gases

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.Comment: 14 pages; v2: major changes (effect of Hartree field included