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 . To analyze the experimental results, the cluster expansion (or fugacity expansion) method is currently under active study . 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 .
To investigate the higher-order terms in the cluster expansion, we generalize the cluster expansion method of Lee and Yang  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 . 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.
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