Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method

Details Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method

2011-12-25

arxiv.org/abs/1112.5768v2

Phys. Rev. A 85, 043601 (2012)

Physics

Condensed Matter

Quantum Gases

21 pages, 10 figures

Scientific paper

10.1103/PhysRevA.85.043601

The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one- and multi-particle reduced density matrices in terms of cluster functions which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.

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