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arXiv · 1310.4665

Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits

Naoyuki Sakumichi·Yusuke Nishida·Masahito Ueda
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Abstract

It is shown that a cluster expansion technique, which is usually applied in the high-temperature regime to calcutate virial coefficients, can be applied to evaluate the superfluid transition temperature of the BCS-BEC crossover à la Lee and Yang. The transition temperature is identified with the emergence of the singularity in the sum of a certain infinite series of cluster functions. In the weak-coupling limit, we reproduce the Thouless criterion and the number equation of Nozières and Schmitt-Rink, and hence the transition temperature of the BCS theory. In the strong-coupling limit, we reproduce the transition temperature of Bose-Einstein condensation of non-interacting tightly bound dimers.

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Naoyuki Sakumichi, Yusuke Nishida, Masahito Ueda. 2014-02-28. Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits. https://doi.org/10.1103/physreva.89.033622

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