Cai Weimin, Guo Hao, He Yan, Chien Chih-Chun
Department of Physics, Southeast University, Nanjing, 211189, China.
College of Physical Science and Technology, Sichuan University, Chengdu, Sichuan, 610064, China.
Sci Rep. 2018 Mar 5;8(1):3981. doi: 10.1038/s41598-018-22273-1.
The shear viscosity has been an important topic in ultracold Fermi gases, and it has served as a diagnostic of various theories. Due to the complicated phase structures of population-imbalanced (polarized) Fermi gases with tunable attraction, past works on the shear viscosity mainly focused on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi superfluid at finite temperatures by a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. The Cooper pairs lead to the anomalous shear viscosity analogous to the shear viscosity. We derive an exact relation connecting certain thermodynamic quantities and transport coefficients at the mean-field level for polarized unitary Fermi superfluids. An approximate relation beyond mean-field is proposed and only exhibits mild deviations from our numerical results. In the unitary and Bose-Einstein condensation (BEC) regimes, the total shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. Moreover, competition among the excess fermions, noncondensed pairs, and fermionic quasiparticles may lead to non-monotonic behavior of the ratio between the shear viscosity and relaxation time as the polarization increases.
剪切粘度一直是超冷费米气体中的一个重要课题，它可用于检验各种理论。由于具有可调吸引力的粒子数不平衡（极化）费米气体的相结构复杂，以往关于剪切粘度的研究主要集中在非极化费米气体上。在此，我们通过用于热力学量的配对涨落理论和用于输运系数的规范不变线性响应理论，研究了有限温度下均匀的、粒子数不平衡的费米超流体的剪切粘度。库珀对导致了类似于剪切粘度的反常剪切粘度。我们推导了极化幺正费米超流体在平均场水平下连接某些热力学量和输运系数的精确关系。提出了一个超出平均场的近似关系，它与我们的数值结果仅表现出轻微偏差。在幺正和玻色 - 爱因斯坦凝聚（BEC）区域，总剪切粘度随极化增加，因为过量的多数费米子会引起无隙激发，其行为类似于正常流体。此外，随着极化增加，过量费米子、非凝聚对和费米子准粒子之间的竞争可能导致剪切粘度与弛豫时间之比出现非单调行为。
