Perron-Frobenius theorem on the superfluid transition of an ultracold Fermi gas

Naoyuki Sakumichi; Norio Kawakami; Masahito Ueda

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arXiv · 1202.6532

Perron-Frobenius theorem on the superfluid transition of an ultracold Fermi gas

Naoyuki Sakumichi·Norio Kawakami·Masahito Ueda

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Abstract

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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Naoyuki Sakumichi, Norio Kawakami, Masahito Ueda. 2012-02-29. Perron-Frobenius theorem on the superfluid transition of an ultracold Fermi gas. https://arxiv.org/abs/1202.6532

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