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arXiv 1704.01628cond-mat.stat-mechcond-mat.quant-gasmath-phmath.MP
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有限温度下囚禁费米气体的动能

Kinetic energy of a trapped Fermi gas at finite temperature

Jacek Grela, Satya N. Majumdar, Gregory Schehr

摘要:

本文研究了在有限温度下,在频率为$T$的$1d$谐振阱中,$N$非相互作用费米子的动能(或等效势能)的统计特性。值得注意的是,我们找到了一个精确的解决方案,在任何温度$T$和任何$N$,使用非平凡的映射到一个可积的Calogero-Moser-Sutherland模型的动能的完整分布。作为温度$T$的函数,对于大的$N$,我们确定:(i)一个量子制度,对于$T \sim \hbar ω$,其中量子波动占主导地位,以及(ii)一个热制度,对于$T \sim N \hbar ω$,由热波动支配。我们展示了如何平均值,方差以及大偏差函数与分布的动能交叉从量子的热制度,随着温度的增加。

英文摘要:

We study the statistics of the kinetic (or equivalently potential) energy for $N$ non-interacting fermions in a $1d$ harmonic trap of frequency $ω$, at finite temperature $T$. Remarkably, we find an exact solution for the full distribution of the kinetic energy, at any temperature $T$ and for any $N$, using a non-trivial mapping to an integrable Calogero-Moser-Sutherland model. As a function of temperature $T$, and for large $N$, we identify: (i) a quantum regime, for $T \sim \hbar ω$, where quantum fluctuations dominate and (ii) a thermal regime, for $T \sim N \hbar ω$, governed by thermal fluctuations. We show how the mean, the variance as well as the large deviation function associated with the distribution of the kinetic energy cross over from the quantum to the thermal regime as temperature increases.

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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