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arXiv 1305.0657cond-mat.quant-gascond-mat.stat-mechcond-mat.str-el
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稀玻色气体的基态能量和凝析密度

Ground-State Energy and Condensate Density of a Dilute Bose Gas Revisited

Kazumasa Tsutsui, Takafumi Kita

备注：
5 pages, 3 figures
发表信息：
J. Phys. Soc. Jpn. 82, 063001 (2013)
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摘要：

采用同时满足Hugenholtz-Pines定理和守恒律的自洽微扰展开，研究了稀玻色气体的每粒子基态能量$E/N$和凝聚密度$n_0$.目前还没有考虑到的一类自能费曼图，被证明是在Lee、Huang和Yang [Phys. Rev. 106，1135（1957）]报道的表达式中增加了一个额外的常数$c_{ip}\sim O(1)$，即$E/N=(2π\hbar^2 an/m)[1+(128/15\sqrt{π}+16c_{ip}/5)\sqrt{a^3n}]$和$n_0/n=1-(8/3\sqrt{π}+c_{ip})\sqrt{a^3n}$，其中$a$、$n$和$m$分别是s波散射长度、粒子密度和粒子质量。我们提出了一对夫妇的估计$c_{ip}$，三阶微扰展开产生$c_{ip}=0.412$。

英文摘要：

The ground-state energy per particle $E/N$ and condensate density $n_0$ of a dilute Bose gas are studied with a self-consistent perturbation expansion satisfying the Hugenholtz-Pines theorem and conservation laws simultaneously. A class of Feynman diagrams for the self-energy, which has escaped consideration so far, is shown to add an extra constant $c_{ip}\sim O(1)$ to the expressions reported by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957) ] as $E/N=(2π\hbar^2 an/m)[1+(128/15\sqrt{π}+16c_{ip}/5)\sqrt{a^3n}]$ and $n_0/n=1-(8/3\sqrt{π}+c_{ip})\sqrt{a^3n}$, where $a$, $n$, and $m$ are are the s-wave scattering length, particle density, and particle mass, respectively. We present a couple of estimates for $c_{ip}$; the third-order perturbation expansion yields $c_{ip}=0.412$.

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