论文标题
统一限制附近的三个和四个相同的费米子
Three and four identical fermions near the unitary limit
论文作者
论文摘要
这项工作分析了附近的三个和四个质量质量的费尔米金系统，并使用超球方法分析了$ s $ - 和$ p $ - 波 - 波浪的统一限制。这里解决的统一状态是两体二聚体能量为零的能量。对于$ s $波统一限制附近的费米金系统，$ n $ - 体连续体中的超大电势表现出一个通用的长距离$ r^{ - 3} $行为，由$ s $ - 波散射长度支配。讨论了这种行为对低能相移的含义。在$ p $ - 波统一的限制下，通过定性观察$ l^π= 0^{+} $对称性的单位电势的结构来研究四体系统。定量分析表明，对于这些系统，有最低的高度电势中有四聚体状态。这些四聚体与两体碎片通道中的相应三聚体之间建立了相关性。讨论了与四体重组过程$ \ mathrm {a+a+a+a} \ leftrightArrow \ mathrm {a_3+a} $有关的通用属性。
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.
