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World Journal of Condensed Matter Physics

Transport Properties of Superfluid Dipolar Fermi Gas at Low Temperatures

Maryam Khademi Dehkordi

Published Jan 1, 2014• 0 citations
Publisher

Abstract

Transport coefficients of superfluid dipolar Fermi gas are calculated by using the Boltzmann equation approach. The interaction between Bogoliubov-Bogoliubov quasiparticles in the collision integral is considered in binary process. The shear viscosities nxz↑ = nyy↑,nxy↑; nxz↑ ≈ nyz↑; and nu↑ are proportional to T-6; T-8; and T-10 , respectively. Also, we have found the elements of the diffusive thermal conductivities Kxx↑= Kyy↑ with temperature dependency T-5 and Ku↑ which is proportional to T-7 and other components which are zero.

DOI
10.4236/wjcmp.2014.42010

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The shear viscosity tensor of the superfluid Fermi gas in p-wave state with weak interaction is calculated at low temperatures, by using the Boltzmann equation approach. We consider the transition probabilities for the binary, decay and coalescence processes. We show that only the binary processes are dominated at low temperatures and the components of shear viscosity η_xy, η_xx, η_yy are proportional to (1/T)^2, and η_xz, η_yz and η_zz are proportional to (1/T)^4 and (1/T)^6, respectively.
We derive the Boltzmann equation describing long-wavelength low-frequency transport and relaxation processes in a superfluid Fermi liquid close to the transition temperature Tc{T}_{c}Tc​. In the superfluid, the quasiparticle number is not conserved and therefore one has to take into account the decay of one quasiparticle into three and the inverse process, as well as the two-quasiparticle scattering process. We calculate the collision term in the Boltzmann equation to first order in the superfluid gap $\ensuremath{\Delta}$ and show that it is related rather simply to the corresponding normal-state collision term. As applications of the Boltzmann equation, we solve it exactly to calculate the shear viscosity, and the intrinsic spin relaxation rate. The shear viscosity drops as $\ensuremath{\Delta}\ensuremath{\propto}{({T}_{c}\ensuremath{-}T)}^{\frac{1}{2}}$ for temperatures just below Tc{T}_{c}Tc​, and we determine the coefficient of $\ensuremath{\Delta}$ as a function of the normal-state collision probability. Leggett and Takagi's characteristic spin-relaxation time is shown to be equal to the relaxation time of a normal-state quasiparticle at the Fermi energy at Tc{T}_{c}Tc​. The results provide one with a useful consistency check on experimental measurements which is independent of any assumption about the normal-state collision probability.
We compute the shear viscosity, thermal conductivity, and spin diffusivity of a Fermi gas with short-range interactions in the Fermi liquid regime of the normal phase, that is, at temperatures T much lower than the Fermi temperature T_{F} and larger than the superfluid critical temperature T_{c}. In line with recent advances in the precision of cold atom experiments, we provide exact results up to the second order in the interaction strength. We extend the Landau-Salpeter equation to compute the collision amplitude beyond the forward-scattering limit, covering all collisions on the Fermi surface. We treat the collision kernel exactly, leading to significant corrections beyond relaxation-time or variational approximations. The transport coefficients, as functions of the s wave scattering length a and Fermi wave number k_{F}, follow (1+γk_{F}a)/a^{2} up to corrections of order O(a^{0}), with a positive coefficient γ for the viscosity and negative one for the thermal conductivity and spin diffusivity.