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World Journal of Condensed Matter Physics

Shear Viscosity of a Superfluid Dipolar Gas at Low Temperatures

Maryam Khademi Dehkordi

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We compute the shear viscosity of superfluid Bose and Fermi gases on the base of Boltzmann equation and relaxation times. We show that, in the low temperature limit, the shear viscosities of Bose and Fermi gases are proportional to T-1evp0/T and T-4, respectively. For the superfluid Bose gas at low temperature limit, only splitting processes contribute to the shear viscosity.

DOI
10.4236/wjcmp.2014.41007

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We compute the shear viscosity of superfluid Bose and Fermi gases on the base of Boltzmann equation and relaxation times. We show that, in the low temperature limit, the shear viscosities of Bose and Fermi gases are proportional to T-1evp0/T and T-4, respectively. For the superfluid Bose gas at low temperature limit, only splitting processes contribute to the shear viscosity.
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.
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.
We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature TTT limit the shear viscosity scales as ${\ensuremath{\xi}}^{5}∕{T}^{5}$, where the universal parameter $\ensuremath{\xi}$ relates the chemical potential and the Fermi energy, $\ensuremath{\mu}=\ensuremath{\xi}{\ensuremath{\epsilon}}_{F}$. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature Tc{T}_{c}Tc​. A na\"{\i}ve extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of $\ensuremath{\sim}5$ of the proposed bound $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.
We derive the Boltzmann equation for relaxation rate, viscosity and thermal conductivity in ultra cold normal dipolar bose gas. We use anisotropic dipole- dipole interaction. We obtain the temperature dependence of the relaxation rate and give formal expressions for the shear viscosity and thermal conductivity coefficients. These coefficients are proportional to . The different form of potentials in calculations show themselves in the coefficients of the viscosity and thermal conductivity. The ratio of the viscosity coefficient for dipole-dipole interaction to contact potential is three order and this ratio for thermal conductivity is two order.
We analyze the contributions of Nambu-Goldstone modes to the shear viscosity of a superfluid atomic Fermi gas close to unitarity. We show that the low temperature experimental values of the shear viscosity to entropy ratio, η/sη/sη/s, are reproduced considering an effective shear viscosity which takes into account the collisions among Nambu-Goldstone bosons and the finite size of the optical trap. We predict that, for T≲0.1TFT \lesssim 0.1 T_FT≲0.1TF​, η/sη/sη/s should correlate with the size of the trap and linearly decrease with decreasing temperature. For T≳0.1TFT \gtrsim 0.1 T_FT≳0.1TF​, we find agreement with the experimental data assuming that the Nambu-Goldstone modes have an anomalous dispersion law.
We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity η(ω)\eta(\omega)η(ω) exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of 0.5TF0.5 T_F0.5TF​, thus invalidating a quasiparticle description. The ratio η/s\eta/sη/s between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound ℏ/(4πkB)\hbar/(4\pi k_B)ℏ/(4πkB​) by a factor of about seven.