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arXiv 1606.00512cond-mat.quant-gasquant-ph
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非均匀动力学平均场论的广义梯度展开：对谐波势阱中超冷原子的应用

Generalized gradient expansion for inhomogeneous dynamical mean-field theory: Application to ultracold atoms in a harmonic trap

J. K. Freericks, Shuyang Han, Karlis Mikelsons, H. R. Krishnamurthy

备注：
(14 pages, 6 figures, submitted to Phys. Rev. A)
发表信息：
Phys. Rev. A 94, 023614 (2016)
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摘要：

本文将非均匀动力学平均场论方法推广到势阱中超冷原子性质的研究。这种方法超越了众所周知的局域密度近似，并且在更高的温度下，在正常相中，它显示了为什么局域密度近似工作得如此好，因为局域密度近似和广义梯度近似基本上彼此无法区分（并且与完全非均匀动力学平均场论内的精确解无法区分）。但是，由于广义梯度展开只涉及最近邻修正，当系统进入有序相时，它在低温下不起作用。这主要是由于有序相经常满足一些全局约束的问题，这些约束决定了空间有序模式，而局部密度和广义梯度近似不能施加这些约束;它们也高估了有序的趋势。该理论被应用到相分离的不同质量的费米子的混合物所代表的Falicov-Kimball模型和确定熵的每粒子的费米子系统所代表的哈伯德模型。广义梯度近似是局部密度近似准确性的一个有用的诊断--当两种方法一致时，它们可能是准确的，当它们不一致时，两者都不可能是正确的。

英文摘要：

We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher temperatures, in the normal phase, it shows why the local density approximation works so well, since the local density and generalized gradient approximations are essentially indistinguishable from each other (and from the exact solution within full inhomogeneous dynamical mean-field theory). But because the generalized gradient expansion only involves nearest-neighbor corrections, it does not work as well at low temperatures, when the systems enter into ordered phases. This is primarily due to the problem that ordered phases often satisfy some global constraints which determine the spatial ordering pattern, and the local density and generalized gradient approximations are not able to impose those kinds of constraints; they also overestimate the tendency to order. The theory is applied to phase separation of different mass fermionic mixtures represented by the Falicov-Kimball model and to determining the entropy per particle of a fermionic system represented by the Hubbard model. The generalized gradient approximation is a useful diagnostic for the accuracy of the local density approximation---when both methods agree, they are likely accurate, when they disagree, neither is likely to be correct.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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