有限温度下幺正费米气体的动量分布和接触
The unitary Fermi gas at finite temperature: momentum distribution and contact
摘要：
幺正费米气体（UFG）是迄今为止已知的最强相互作用的系统之一，因为它饱和了量子力学散射截面上的幺正束缚。在短相互作用范围和大散射长度的限制下，UFG对应于双组分费米气体，目前在超冷原子实验中通过费什巴赫共振实现。虽然很容易定义，但UFG提出了一个具有挑战性的量子多体问题，因为它除了密度之外没有任何特征尺度。因此，准确的定量预测的热力学性质的UFG需要Monte Carlo计算。然而，在纯分析方法方面也取得了重大进展。值得注意的是，在2005年，Tan推导出了一组精确的热力学关系，其中一个被称为“接触”C的普适量起着至关重要的作用。最近，C也被发现确定高频幂律衰减的前因子，以及剪切和体积粘度总和规则的右手侧。因此，接触是关于处于平衡以及远离平衡的UFG的中心信息。在这次演讲中，我们描述了费米气体在幺正性和周围的一些已知方面，展示了我们最新的Monte Carlo结果在有限温度下的接触，并总结了该领域的开放问题，其中一些我们开始回答使用大规模Monte Carlo计算通过适应方法从格点量子色动力学。
英文摘要：
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.
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