We investigate the temperature dependence of the shear viscosity and spin diffusion in a two-dimensional Fermi gas with contact interactions, as realized in ultracold atomic gases. We describe the transport coefficients in terms of a Boltzmann equation and present a full numerical solution for the degenerate gas. In contrast to previous works we take the medium effects due to finite density fully into account. This effect reduces the viscosity-to-entropy ratio $\ensuremath{\eta}/s$ by a factor of 3, and similarly for spin diffusion. The trap-averaged viscosity agrees well with recent measurements by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].
The longitudinal relaxation time T
sb1 is calculated for a dilute Fermi gas. We include the possibility of arbitrary degrees of polarization P, and uniform external magnetic fields. At low temperatures T
sb1 is proportional to T
sp−2 for the unpolarized gas in agreement with earlier calculations. For a polarized system in zero applied field the separation between up and down Fermi spheres provides an open channel in phase space for spin flipping processes. As temperature is reduced to zero T
sb1 levels off and approaches a constant value which depends sensitively on P, leading to much smaller values of T
sb1 than in the unpolarized case. For relaxation in a uniform external field H, Zeeman energy conservation during spin flipping interactions essentially shifts the location of the T
sp−2 behavior from zero polarization to the polarization P(H) which would be produced in equilibrium with the external field H. When the initial polarization of the system is different from P(H), T
sb1 again approaches a constant value which is equally sensitive to the initial polarization as temperature is reduced to zero. We apply our calculations to the case of dilute
sp3He-HeII solutions. We also consider the calculation of density dependent corrections to T
sb1 for unpolarized, or weakly polarized
sp3He-HeII using the long wavelength limit of the Bardeen-Baym-Pines interaction as a form for the spin independent part of the
sp3He-
sp3He interaction. Owing to the positive sign of the antisymmetric Landau parameter
rmFsbspoa in dilute
sp3He-HeII Fermi Liquid interactions act to screen the magnetic dipole interactions which cause relaxation. To lowest order in density we find that the relaxation rate 1/T
sb1 is reduced by factor
rm(1−3Fsbspoa) which compares favorably with recent calculations of T
sb1 for pure
sp3He.
The transport properties of one-dimensional Fermi gases at low temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipative effects, one needs to examine interactions beyond the LL model. In this work, we provide a simple model that allows for a direct microscopic calculation of the bulk viscosity, namely, the one-dimensional spin polarized
p-wave Fermi gas. To leading order in the finite interaction strength, we find that the bulk viscosity is finite and consistent with the requirement of scale symmetry. We further show that the bulk viscosity satisfies the Bose-Fermi duality relating the weakly interacting limit of the spin polarized Fermi gas to the strongly interacting limit of the Lieb-Liniger model and vice versa. This work establishes the bulk viscosity to leading order in scale-breaking interactions in both the strongly and weakly interacting limits for both high and low temperatures.
The aim of this work is to study a dilute Fermi gas, whether it has a spin 1/2 or it has a high degeneracy. The starting point is to calculate the energy of the system. However, as we are dealing with a many body system, a perturbation series method will be applied. R. F. Bishop in reference [1] wrote the terms of the expansion up to fourth order in the gas parameter, which is defined as the Fermi momentum times the S-wave scattering length, but only for the case of a non-polarized gas. What we do in this present work is the generalization of that expansion up to third order including any possible polarization. The universal expansion, that is up to second order, have been computed analytically. For the third order terms was not possible, but thanks to numerical calculation we have obtained the energy for different polarizations. Therefore, this work will contain a combination of both analytical and numerical calculus. The final expression obtained for the energy depends on the polarization, the gas parameter and the degeneracy and stands for low density gases. Afterwards, thanks to knowing the relation between the energy and the polarization, the study of the ferromagnetic phase transition is presented. We see how the transition point changes due to the degeneracy and what kind of phase transition we obtain. For spin 1/2 a continuous transition is observed, while a discontinuous transition happens for higher degeneracy. To complement the phase transition study, different physical properties have been computed, such as, the magnetic susceptibility, and the Tan?s constant. Our study is extended to highly degenerate Fermi gases which are now realized in cold Fermi labs.
Abstract Very dilute solutions of 3He in superfluid 4He behave as an almost ideal Fermi gas at millikelvin temperatures, which can be strongly polarized in high magnetic fields. This has enabled studies of their equilibrium, transport, and dynamical spin properties to be made over a wide range of temperatures, concentrations, and polarizations covering systems that are highly degenerate to those that are non-degenerate. This chapter discusses polarized Fermi gas, model theories, equilibrium theories, transport properties, and spin dynamics.
We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.