Attractive $p$-wave one-dimensional fermions are studied in the fermionic Tonks-Girardeau regime in which the diagonal properties are shared with those of an ideal Bose gas. We study the off-diagonal properties and present analytical expressions for the eigenvalues of the one-body density matrix. One striking aspect is the universality of the occupation numbers which are independent of the specific shape of the external potential. We show that the occupation of natural orbitals occurs in pairs, indicating the formation of composite bosons, each consisting of two attractive fermions. The formation of composite bosons sheds light on the pairing mechanism of the system orbitals, yielding a total density equal to that of a Bose-Einstein condensate.

中文翻译：

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强相互作用一维费米子系统中通用复合玻色子的形成

吸引人的$p$在费米子 Tonks-Girardeau 体系中研究了波一维费米子，其中对角线性质与理想玻色气体的对角线性质相同。我们研究了非对角线性质并提出了单体密度矩阵特征值的解析表达式。一个引人注目的方面是职业数量的普遍性，它与外部潜力的具体形状无关。我们表明，自然轨道的占据是成对发生的，表明复合玻色子的形成，每个玻色子由两个有吸引力的费米子组成。复合玻色子的形成揭示了系统轨道的配对机制，产生的总密度等于玻色-爱因斯坦凝聚体的密度。