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arXiv 0910.4878cond-mat.quant-gas
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具有么正性和平方反比相互作用的冷原子

Cold atoms at unitarity and inverse square interaction

R. K. Bhaduri, M. V. N. Murthy, M. K. Srivastava

摘要:

考虑球谐振子中两个全同原子与零程相互作用,该相互作用被调谐为产生s波零能束缚态。已知系统的量子谱是精确可解的。我们注意到,相同的分波量子谱是由一维标度不变的平方反比势得到的。长期以来被称为Calogero-Sutherland-Moser(CSM)模型,它导致了Halfman和Wu的分数排除统计(FES)。统计参数推导出从解析计算的第二维里系数。当FES应用于具有么正性的费米气体时,在不使用任何自由参数的情况下,它给出了与实验数据很好的一致性。

英文摘要:

Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero-Sutherland-Moser (CSM) model, it leads to Fractional Exclusion Statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.

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