Dynamics of a trapped Fermi gas in the BCS phase

Abstract

We derive semiclassical transport equations for a trapped atomic Fermi gas in the BCS phase at temperatures between zero and the superfluid transition temperature. These equations interpolate between the two well-known limiting cases of superfluid hydrodynamics at zero temperature and the Vlasov equation at the critical one. The linearized version of these equations, valid for small deviations from equilibrium, is worked out and applied to two simple examples where analytical solutions can be found: a sound wave in a uniform medium and the quadrupole excitation in a spherical harmonic trap. In spite of some simplifying approximations, the main qualitative results of quantum mechanical calculations are reproduced, which are the different frequencies of the quadrupole mode at zero and the critical temperature and strong Landau damping at intermediate temperatures. In addition we suggest a numerical method for solving the semiclassical equations without further approximations.

15 pages, 4 figures; v2: discussion and references added; v3: typos in Eqs. (6), (33), (34b), and (61) corrected

References in corpus (7)

• Collective excitations of a degenerate gas at the BEC-BCS crossover
• Breakdown of Hydrodynamics in the Radial Breathing Mode of a Strongly-Interacting Fermi Gas
• Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit
• Temperature and finite-size effects in collective modes of superfluid Fermi gases
• Two-fluid model for a rotating trapped Fermi gas in the BCS phase
• Transition to hydrodynamics in colliding fermion clouds
• Collisions and expansion of an ultracold dilute Fermi gas

Cited by in corpus (18)

• Theory of ultracold Fermi gases
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Superfluid hydrodynamics in the inner crust of neutron stars
• Time Dependent Pairing Equations for Seniority One Nuclear Systems
• Numerical solution of the Boltzmann equation for the collective modes of trapped Fermi gases
• Direct Simulation Monte Carlo method for cold atom dynamics: classical Boltzmann equation in the quantum collision regime
• Collective modes of trapped Fermi gases with in-medium interaction
• Collective excitations in the neutron star inner crust
• Finite temperature damping of collective modes of a BCS-BEC crossover superfluid
• Coupling of hydrodynamics and quasiparticle motion in collective modes of superfluid trapped Fermi gases
• Radial quadrupole and scissors modes in trapped Fermi gases across the BCS phase transition
• Self-consistency and collective effects in semiclassical pairing theory
• Kinetic equation for finite systems of fermions with pairing
• Nuclear collective dynamics within Vlasov approach
• Sound wave propagation in strongly elongated fermion clouds at finite collisionality
• Low-energy modes of spin-imbalanced Fermi gases in BCS phase
• Dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap
• Hamiltonian formulation of the effective kinetic theory for superfluid Fermi liquids