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Criteria of Off-Diagonal Long-Range Order in Bose and Fermi Systems Based on the Lee-Yang Cluster Expansion Method

Dr Naoyuki Sakumichi

Department of Physics, The University of Tokyo, Japan

3:30 pm Friday, 8 March 2013, EN313 Lecture Theatre (EN Building), Hawthorn.


The equation of state for the unitary Fermi gas has recently been measured by using an ultracold atomic gas [1]. To analyze the experimental results, the cluster expansion (or fugacity expansion) method is currently under active study [2]. Most previous theoretical studies focus on the calculation of the low-order (up to the fourth order) cluster integrals. However, the low-order cluster expansion and experimental data are consistent only for the fugacity is smaller than unity, whereas the critical fugacity of the superfluid phase transition is greater than 10 [1].

To investigate the higher-order terms in the cluster expansion, we generalize the cluster expansion method of Lee and Yang [3] and identify the criteria of the off-diagonal long-range order (ODLRO) of the reduced density matrices in Bose and Fermi systems based on the Lee-Yang cluster expansion method [4]. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one-particle and multiparticle reduced density matrices in terms of cluster functions, which are defined for the same system with Boltzmann statistics.


[1] M. Horikoshi et al., Science 327, 442 (2010); S. Nascimbène et al., Nature 463, 1057 (2010); M. J. H. Kuetal., Science, 335, 563 (2012).

[2] X.-J. Liu, H. Hu and P. D. Drummond, PRL 102, 160401 (2009); PRA 82, 023619 (2010); X. Leyronas, PRA 84, 053633 (2011); D. Rakshit, K. M. Daily and D. Blume, PRA 85, 033634 (2012).

[3] T. D. Lee and C. N.Yang, Phys. Rev. 113, 1165 (1958); 117, 22 (1960).

[4] N. Sakumichi, N. Kawakami and M. Ueda, Phys. Rev. A 85, 043601 (2012).

[5] N. Sakumichi, N. Kawakami and M. Ueda, arXiv:1202.6532 (2012).



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