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arXiv 1601.02206cond-mat.quant-gas
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一维相互作用玻色子系统中的玻色-爱因斯坦凝聚

Bose-Einstein condensation in a one-dimensional system of interacting bosons

Maksim Tomchenko

备注：
16 pages, 2 figures. v1: published version; v2: we add a Fig. 2, which is absent in the published version
发表信息：
J. Low Temp. Phys. 182, 170 (2016)
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摘要：

利用密度矩阵的Vakarchuk公式，计算了一维均匀周期相互作用玻色子系统基态动量为\hbar k的原子数N_k。对于不可穿透的点玻色子，我们得到N_0 = 2 \sqrt{N}和N_{k=2πj/L} = 0.31 N_{0} / \sqrt{|j|} .也就是说，在大N时，在低水平上没有凝析油或准凝析油。对于弱耦合几乎点玻色子（β= \frac{ν_{0}m}{π^{2}\hbar^{2}n} \ll 1），我们得到了N_{0} /N =（\frac{2}{N\sqrtβ}）^{ \sqrt β/2}和N_{k=2πj/L} = \frac{N_0\sqrtβ}{4|j|^{1-\sqrtβ/2}} .在这种情况下，如果N大并且$β$小，则准冷凝物存在于k=0的水平上并且存在于k \neq为0的低水平上（例如，对于N = 10^{10}，β= 0.01）。提出了一种测量这种碎裂准凝聚体的方法。

英文摘要：

Using the Vakarchuk formulae for the density matrix, we calculate the number N_k of atoms with momentum \hbar k for the ground state of a uniform one-dimensional periodic system of interacting bosons. We obtain for impenetrable point bosons N_0 = 2\sqrt{N} and N_{k=2πj/L} = 0.31N_{0}/\sqrt{|j|}. That is, there is no condensate or quasicondensate on low levels at large N. For almost point bosons with weak coupling (β=\frac{ν_{0}m}{π^{2}\hbar^{2}n} \ll 1), we obtain N_{0}/N = (\frac{2}{N\sqrtβ})^{\sqrtβ/2} and N_{k=2πj/L} = \frac{N_0\sqrtβ}{4|j|^{1-\sqrtβ/2}}. In this case, the quasicondensate exists on the level with k=0 and on low levels with k\neq 0, if N is large and $β$ is small (e.g., for N = 10^{10}, β= 0.01). A method of measurement of such fragmented quasicondensate is proposed.

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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