We calculate the damping of the Bogoliubov–Anderson mode in a one-dimensional (1D) two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther–Emery liquid of weakly bound pairs to a Lieb–Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks–Girardeau gas with a universal constant α ζ = 0.38 in the viscosity ζ = α ζ ℏ n for T = 0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.We calculate the damping of the Bogoliubov–Anderson mode in a one-dimensional (1D) two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther–Emery liquid of weakly bound pairs to a Lieb–Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks–Girardeau gas with a universal constant α ζ = 0.38 in the viscosity ζ = α ζ ℏ n for T = 0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.

arXiv:cond-mat/0605413New Journal of PhysicsAug 30, 200620 citations

Shear viscosity and damping of collective modes in a two-dimensional Fermi gas

Thomas Schäfer

The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length ${a}_{2\mathrm{d}}$ in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length ${a}_{2\mathrm{d}}$ in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].

arXiv:1111.7242Physical Review AMar 19, 201236 citations

Scale Invariance and Viscosity of a Two-Dimensional Fermi Gas

Enrico Vogt, Michael Feld, Bernd Fröhlich +3 more

We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.

arXiv:1111.1173Physical Review LettersFeb 17, 2012157 citations

The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length

{a}_{2\mathrm{d}}

in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].