Shao-Jian Jiang, Wu-Ming Liu, G. W. Semenoff, Fei Zhou
Bose gases at large scattering lengths or near resonances, where the standard dilute gas theory breaks down, have posed a long-standing challenge for quantum many-body physics. In this Letter, we offer an answer to this enigmatic topic of quantum gases at large scattering lengths. We should outline a rigorous solution to Bose gases near resonance which we obtain by using an epsilon expansion near four spatial dimension. In dimension d = 4 - epsilon, the chemical potential of Bose gases near resonances is shown to approach the universal value epsilon^(2/(4-epsilon)) epsilon_F sqrt(2/3) (1 + 0.474 epsilon - i 1.217 epsilon + ...), where epsilon_F is the Fermi energy defined for a Fermi gas of density n, and the condensation fraction is equal to 2/3 (1 + 0.0877 epsilon + ...). This is in contrast to three spatial dimension where the chemical potential further depends on a non-universal ultraviolet length scale due to Efimov physics.
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http://arxiv.org/abs/1307.4263
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