幺正费米气体、牛顿展开和非相对论性共形场论
Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories
摘要：
本文综述了在超冷原子实验中实现的幺正费米气体的理论研究进展。首先，我们介绍了基于系统的扩展在空间的维度的基础上的扩展技术。我们应用这种方法计算了UFG的热力学量、准粒子谱和临界温度。然后，我们讨论的规模和共形不变性的UFG的后果。证明了非相对论性共形场论中的原算符与谐振势中的能量本征态之间的对应关系。我们利用这种对应关系计算了谐振势中幺正费米子的能量。尺度不变性、共形不变性和广义坐标不变性共同限制了超网格的性质。我们显示了消失的体积粘度的UFG，并推导出低能量的有效拉格朗日超流UFG。最后，我们提出了其他系统的非相对论标度和共形对称性，可以在原则上实现的超冷原子实验。
英文摘要：
We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle spectrum, and the critical temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.
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