In order to generalize the equations of hydrodynamics to a superfluid degenerate Fermi gas the effect of the external gas volume on the momentum of the observed volume of the medium, caused by correlation of the particle momenta, is taken into consideration.
Abstract. We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1, 2, 3, 4] and provide vital tools to study nonequilibrium dynamics of electronic systems. The method we developed is based only on Wick’s theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form. Quantum hydrodynamics and nonlinear differential equations... 2 1.
We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1–4] and provide vital tools for studying non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form.
A system of hydrodynamic equations has been obtained for superfluid Fermi systems with singlet pairing and nonzero momentum which are formed, e.g., in the case of small polarization of the spin system. As a result, the energy gap is a periodic function of the coordinates and a spin-density wave is formed. For such systems the complete set of dynamic variables includes both purely hydrodynamic (superfluid and normal) velocities and the displacement vector corresponding to the violations of the translational invariance. All of the tensors of normal and superfluid densities that appear in the system as well as the elastic moduli have been calculated. A dispersion relation has been obtained for thermal vibrations (second sound) and elastic vibrations, and this relation has turned out to be substantially anisotropic. Observation of the predicted effects is most probable in 3He–He II solutions in magnetic fields of the order of several kilooersteds at low temperatures.
Abstract This chapter is devoted to discussing relevant dynamical and superfluid phenomena exhibited by interacting Fermi gases at low temperatures, with special focus on the strongly interacting Fermi gas at unitarity. The chapter discusses the predictions of hydrodynamic theory concerning the propagation of sound, the collective oscillations and the expansion of the gas after release of the trap. The Landau criterion for superfluidity and the behaviour of the dynamic structure factor are discussed. It also provides some considerations on the radiofrequency transitions as a method to observe pair-breaking transitions and to measure the pairing gap. The chapter discusses the behaviour of two-fluid hydrodynamics and the propagation of second sound as a tool to measure the superfluid density of interacting Fermi gases. It finally provides a brief summary of the rotational properties of the superfluid Fermi gas, like the quenching of the moment of inertia and the occurrence of quantized vortices.
In summary, we use all-optical methods with evaporative cooling near a Feshbach resonance to produce a strongly interacting degenerate Fermi gas. We observe hydrodynamic behavior in the expansion dynamics. At low temperatures, collisions may not explain the expansion dynamics. We observe hydrodynamics in the trapped gas. Our observations include collisionally-damped excitation spectra at high temperature which were not discussed above. In addition, we observe weakly damped breathing modes at low temperature. The observed temperature dependence of the damping time and hydrodynamic frequency are not consistent with collisional dynamics nor with collisionless mean field interactions. These observations constitute the first evidence for superfluid hydrodynamics in a Fermi gas.
We report on the observation of a highly degenerate, strongly interacting Fermi gas of atoms. Fermionic lithium-6 atoms in an optical trap are evaporatively cooled to degeneracy using a magnetic field to induce strong, resonant interactions. Upon abruptly releasing the cloud from the trap, the gas is observed to expand rapidly in the transverse direction while remaining nearly stationary in the axial direction. We interpret the expansion dynamics in terms of collisionless superfluid and collisional hydrodynamics. For the data taken at the longest evaporation times, we find that collisional hydrodynamics does not provide a satisfactory explanation, whereas superfluidity is plausible.