超冷费米气体超流相变的Perron-Frobenius定理
Perron-Frobenius theorem on the superfluid transition of an ultracold Fermi gas
摘要：
应用Perron-Frobenius定理研究了具有零程s波相互作用的二组分费米气体的超流相变。根据Lee和Yang的量子集团展开方法，将巨配分函数用Lee-Yang压缩0-图表示。研究了梯形Lee-Yang压缩0-图的无穷级数的奇异性。我们指出，奇异性是由Perron-Frobenius本征值的某一原始矩阵，这是定义的两体集团函数和费米分布函数。结果表明，在相变点处存在唯一的逸度，这意味着在Lee-Yang收缩0-图的梯形近似水平下，二聚体和库珀对的玻色-爱因斯坦凝聚体不存在碎裂.并应用于强束缚二聚体的玻色-爱因斯坦凝聚体。
英文摘要：
The Perron-Frobenius theorem is applied to identify the superfluid transition of a two-component Fermi gas with a zero-range s-wave interaction. According to the quantum cluster expansion method of Lee and Yang, the grand partition function is expressed by the Lee-Yang contracted 0-graphs. A singularity of an infinite series of ladder-type Lee-Yang contracted 0-graphs is analyzed. We point out that the singularity is governed by the Perron-Frobenius eigenvalue of a certain primitive matrix which is defined in terms of the two-body cluster functions and the Fermi distribution functions. As a consequence, it is found that there exists a unique fugacity at the phase transition point, which implies that there is no fragmentation of Bose-Einstein condensates of dimers and Cooper pairs at the ladder-approximation level of Lee-Yang contracted 0-graphs. An application to a Bose-Einstein condensate of strongly bounded dimers is also made.
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