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arXiv 1011.3845cond-mat.quant-gas
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有限温度下强相互作用费米子的万有接触

Universal contact of strongly interacting fermions at finite temperatures

Hui Hu, Xia-Ji Liu, Peter D. Drummond

备注：
15 pages, 10 figures
发表信息：
New J.Phys.13:035007,2011
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摘要：

最近发现的稀释的、强相互作用的费米气体的普遍热力学行为也暗示了短距离多体对关联函数中的普遍结构，正如接触${\cal I}$所量化的那样。这个量是这些系统中存在强相关性的一个很好的指标，这为其他强相关量子流体提供了一个高度可访问的物理模型。本文从理论上计算了自由空间和谐波阱中费米气体的这种普遍接触对温度的依赖关系。在费米简并温度$T\gtrsim T_{F}$以上的高温下，我们得到了一个可靠的非微扰量子维里展开到三阶。在低温下，我们比较不同的近似强耦合理论。这些都做出了不同的预测，需要通过未来的实验或先进的量子蒙特卡罗模拟来验证。我们推测，在普适么正性极限，接触或相关单调减少，随着温度的增加，除非温度是显着低于临界温度，$T\ll T_{c}\sim0.2T_{F}$。我们还简要地讨论了如何测量均匀费米气体和谐振态费米气体中的普适接触。

英文摘要：

The recently discovered universal thermodynamic behaviour of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact ${\cal I}$. This quantity is an excellent indicator of the presence of strong correlations in these systems, which provide a highly accessible physical model for other strongly correlated quantum fluids. Here we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, $T\gtrsim T_{F}$, we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures we compare different approximate strong coupling theories. These make different predictions, which need to be tested either by future experiments or advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, $T\ll T_{c}\sim0.2T_{F}$. We also discuss briefly how to measure the universal contact either in homogeneous or harmonically trapped Fermi gases.

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