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Annals of Physics

The shear viscosity of a trapped Bose-condensed gas

Mohammad Ali Shahzamanian, H. Yavary

Published Feb 16, 2006• 4 citations
Publisher
DOI
10.1016/j.aop.2005.12.011

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We extend our recent work on the two-fluid hydrodynamics of the condensate and non-condensate in a trapped Bose gas by including the dissipation associated with viscosity and thermal conduction. For purposes of illustration, we consider the hydrodynamic modes in the case of a uniform Bose gas. A finite thermal conductivity and shear viscosity give rise to a damping of the first and second sound modes in addition to that found previously due to the lack of diffusive equilibrium between the condensate and non-condensate. The relaxational mode associated with this equilibration process is strongly coupled to thermal fluctuations and reduces to the usual thermal diffusion mode above the Bose-Einstein transition. In contrast to the standard Landau two-fluid hydrodynamics, we predict a damped mode centered at zero frequency, in addition to the usual second sound doublet.

arXiv:cond-mat/9911336•Canadian Journal of Physics•Jan 1, 2000•0 citations
Abstract We report on the measurement of shear viscosity in an ultracold Fermi gas with variable temperatures and tunable interactions. A quadrupole mode excitation in an isotropic harmonic trap is used to quantify the shear viscosity of the quantum gas within the hydrodynamic regime. The shear viscosity of the system as a function of temperature has been investigated, and the results closely align with calculations in the high-temperature limit utilizing a new definition of the cutoff radius. Through an adiabatic sweep across the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover, we find that the minimum value of the shear viscosity, as a function of interaction strength, is significantly shifted toward the BEC side. Furthermore, the behavior of the shear viscosity is asymmetric on both sides of the location of the minimum.
We study the shear viscosity of a dilute Fermi gas as a function of the scattering length in the vicinity of the unitarity limit. The calculation is based on kinetic theory, which provides a systematic approach to transport properties in the limit in which the fugacity $z=n{\ensuremath{\lambda}}^{3}/2$ is small. Here, nnn is the density of the gas and $\ensuremath{\lambda}$ is the thermal wavelength of the fermions. At leading order in the fugacity expansion, the shear viscosity is independent of density, and the minimum shear viscosity is achieved at unitarity. At the next order, medium effects modify the scattering amplitude as well as the quasiparticle energy and velocity. We show that these effects shift the minimum of the shear viscosity to the Bose-Einstein condensation side of the resonance, in agreement with the result of recent experiments.
We extend our recent work on the two-fluid hydrodynamics of the condensate and non-condensate in a trapped Bose gas by including the dissipation associated with viscosity and thermal conduction. For purposes of illustration, we consider the hydrodynamic modes in the case of a uniform Bose gas. A finite thermal conductivity and shear viscosity give rise to a damping of the first and second sound modes in addition to that found previously due to the lack of diffusive equilibrium between the condensate and non-condensate. The relaxational mode associated with this equilibration process is strongly coupled to thermal fluctuations and reduces to the usual thermal diffusion mode above the Bose-Einstein transition. In contrast to the standard Landau two-fluid hydrodynamics, we predict a damped mode centered at zero frequency, in addition to the usual second sound doublet.