Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem

We study a two-component Fermi gas that is so strongly polarized that it remains normal fluid at zero temperature. We calculate the occupation numbers within the particle-particle random-phase approximation, which is similar to the Nozieres-Schmitt-Rink approach. We show that the Luttinger theorem is fulfilled in this approach. We also study the change of the chemical potentials which allows us to extract, in the limit of extreme polarization, the polaron energy.Comment: 8 pages, 8 figure

Superfluid hydrodynamics in the inner crust of neutron stars

The inner crust of neutron stars is supposed to be inhomogeneous and composed of dense structures (clusters) that are immersed in a dilute gas of unbound neutrons. Here we consider spherical clusters forming a BCC crystal and cylindrical rods arranged in a hexagonal lattice. We study the relative motion of these dense structures and the neutron gas using superfluid hydrodynamics. Within this approach, which relies on the assumption that Cooper pairs are small compared to the crystalline structures, we find that the entrainment of neutrons by the clusters is very weak since neutrons of the gas can flow through the clusters. Consequently, we obtain a low effective mass of the clusters and a superfluid density that is even higher than the density of unbound neutrons. Consequences for the constraints from glitch observations are discussed.Comment: 13 pages, 12 figures, figures and discussions added. Accepted in Phys. Rev.

Collective Modes in a Superfluid Neutron Gas within the Quasiparticle Random-Phase Approximation

We study collective excitations in a superfluid neutron gas at zero temperature within the quasiparticle random phase approximation. The particle-hole residual interaction is obtained from a Skyrme functional, while a separable interaction is used in the pairing channel which gives a realistic density dependence of the pairing gap. In accordance with the Goldstone theorem, we find an ungapped collective mode (analogous to the Bogoliubov-Anderson mode). At low momentum, its dispersion relation is approximately linear and its slope coincides with the hydrodynamic speed of sound calculated with the Skyrme equation of state. The response functions are compared with those obtained within the Landau approximation. We also compute the contribution of the collective mode to the specific heat of the neutron gas, which is relevant for the thermodynamic properties of the inner crust of neutron stars.Comment: 12 page

Liquid-gas coexistence vs. energy minimization with respect to the density profile in the inhomogeneous inner crust of neutron stars

We compare two approaches to describe the inner crust of neutron stars: on the one hand, the simple coexistence of a liquid (clusters) and a gas phase, and on the other hand, the energy minimization with respect to the density profile, including Coulomb and surface effects. We find that the phase-coexistence model gives a reasonable description of the densities in the clusters and in the gas, but the precision is not high enough to obtain the correct proton fraction at low baryon densities. We also discuss the surface tension and neutron skin obtained within the energy minimization.Comment: 7 pages, 8 figures, to be published in Phys. Rev.

Polarized Fermi gases at finite temperature in the BCS-BEC crossover

We consider a polarized Fermi gas in the BCS-BEC crossover region above the critical temperature within a T matrix formalism. By treating the mean-field like shift of the quasiparticle energies in a self-consistent manner, we avoid the known pathological behavior of the standard Nozieres-Schmitt-Rink approach in the polarized case, i.e., the polarization has the right sign and the spin polarizability is positive. The momentum distributions of the correlated system are computed and it is shown that, in the zero-temperature limit, they satisfy the Luttinger theorem. Results for the phase diagram, the spin susceptibility, and the compressibility are discussed.Comment: 9 pages; v2: references and comparison with more recent experimental data added; v3: reference added and minor correction

Role of fourth-order phase-space moments in collective modes of trapped Fermi gases

We study the transition from hydrodynamic to collisionless behavior in collective modes of ultracold trapped Fermi gases. To that end, we solve the Boltzmann equation for the trapped Fermi gas via the moments method. We showed previously that it is necessary to go beyond second-order moments if one wants to reproduce the results of a numerical solution of the Boltzmann equation. Here, we will give the detailed description of the method including fourth-order moments. We apply this method to the case of realistic parameters, and compare the results for the radial quadrupole and scissors modes at unitarity to experimental data obtained by the Innsbruck group. It turns out that the inclusion of fourth-order moments clearly improves the agreement with the experimental data. In particular, the fourth-order moments reduce the effect of collisions and therefore partially compensate the effect of the enhanced in-medium cross section at low temperatures.Comment: 10 pages, 2 figures; published versio

Radial quadrupole and scissors modes in trapped Fermi gases across the BCS phase transition

The excitation spectra of the radial quadrupole and scissors modes of ultracold Fermi gases in elongated traps are studied across the BCS superfluid-normal phase transition in the framework of a transport theory for quasiparticles. In the limit of zero temperature, this theory reproduces the results of superfluid hydrodynamics, while in the opposite limit, above the critical temperature, it reduces to the collisionless Vlasov equation. In the intermediate temperature range, the excitation spectra have two or three broad peaks, respectively, which are roughly situated at hydrodynamic and collisionless frequencies, and whose strength is shifted from the hydrodynamic to the collisionless modes with increasing temperature. By fitting the time dependent quadrupole deformation with a damped oscillation of a single frequency, we can understand the "jump" of the frequency of the radial quadrupole mode as a function of interaction strength which has recently been reported by the Innsbruck group.Comment: 6 pages, v2: extended description of the theoretical metho