Abstract We review the BCS (Bardeen–Cooper–Schrieffer)–BEC (Bose–Einstein condensation) crossover phenomenon discussed in an ultracold Fermi atomic gas and a neutron superfluid in the low-density crust regime of a neutron star. A purpose of this paper is to show that these two very different atomic and nuclear systems can be closely related to each other from the viewpoint of this quantum many-body phenomenon. We explain how the BCS–BEC crossover is realized in the former atomic system by using the novel pairing mechanism called Feshbach resonance. We present a simple explanation for this crossover phenomenon to grasp the essence, as well as detailed microscopic theories that can cover the entire BCS–BEC crossover region. In the latter, we point out that the ordinary BCS theory already has the ability to describe the BCS–BEC crossover at T = 0 . At finite temperatures T > 0 , however, we need to go beyond this mean-field theory. Besides general aspects of the BCS–BEC crossover phenomenon, we also pick up special topics peculiar to each atomic gas and neutron fluid. The first one is the pseudogap phenomenon in the normal state of a Fermi atomic gas. The second one is the problem of non-zero effective range in an s -wave neutron superfluid.

中文翻译：

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BCS-BEC 在冷原子和核系统中的交叉

摘要 我们回顾了在超冷费米原子气体和中子星低密度地壳区域中的中子超流体中讨论的 BCS（Bardeen-Cooper-Schrieffer）-BEC（玻色-爱因斯坦凝聚）交叉现象。本文的一个目的是表明，从这种量子多体现象的角度来看，这两个截然不同的原子和核系统可以彼此密切相关。我们解释了如何通过使用称为 Feshbach 共振的新型配对机制在前原子系统中实现 BCS-BEC 交叉。我们对这种交叉现象进行了简单的解释以掌握本质，以及可以覆盖整个 BCS-BEC 交叉区域的详细微观理论。在后者中，我们指出普通 BCS 理论已经具有描述 T = 0 时 BCS-BEC 交叉的能力。然而，在有限温度 T > 0 时，我们需要超越这个平均场理论。除了 BCS-BEC 交叉现象的一般方面，我们还挑选了每种原子气体和中子流体特有的特殊主题。第一个是费米原子气体正常状态下的赝隙现象。第二个是s波中子超流体的非零有效射程问题。