三个和四个相同的费米子接近单位限
Three and four identical fermions near the unitary limit
AI总结：
研究了接近单位限的三个和四个费米子系统的超径势行为及其低能相移特性，揭示了四聚体与三聚体之间的关联。
摘要：
本文分析了在s波和p波单位限附近及处的三个和四个等质量费米子系统，使用超球面方法。此处的单位限是指两体双分子能为零能。对于接近s波单位限的费米子系统，N体连续谱中的超径势表现出受s波散射长度单独控制的长程R^{-3}行为。讨论了这种行为对低能相移的影响。在p波单位限下，通过定性地研究具有L^π=0^{+}对称性的超径势结构来研究四体系统。定量分析显示，这些系统中最低的超径势中存在四聚体状态。将这些四聚体与相应的三聚体在两体碎裂通道中的相关性联系起来。讨论了与四体重组过程A+A+A+A↔A_3+A相关的普遍性质。
英文摘要：
This work analyzes the three and four equal-mass fermionic systems near and at the $s$- and $p$-wave unitary limits using hyperspherical methods. The unitary regime addressed here is where the two-body dimer energy is at zero energy. For fermionic systems near the $s$-wave unitary limit, the hyperradial potentials in the $N$-body continuum exhibit a universal long-range $R^{-3}$ behavior governed by the $s$-wave scattering length alone. The implications of this behavior on the low energy phase shift are discussed. At the $p$-wave unitary limit, the four-body system is studied through a qualitative look at the structure of the hyperradial potentials at unitarity for the $L^π=0^{+}$ symmetry. A quantitative analysis shows that there are tetramer states in the lowest hyperradial potentials for these systems. Correlations are made between these tetramers and the corresponding trimers in the two-body fragmentation channels. Universal properties related to the four-body recombination process $\mathrm{A+A+A+A}\leftrightarrow \mathrm{A_3+A}$ are discussed.
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