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arXiv 2202.07657cond-mat.quant-gasmath-phmath.MPnlin.SI
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有限温度下一维气体中的可动杂质

Mobile impurity in a one-dimensional gas at finite temperatures

Oleksandr Gamayun, Miłosz Panfil, Felipe Taha Sant'Ana

摘要:

我们考虑一维自由费米子气体与单个杂质相互作用的McGuire模型。我们计算了有限温度下杂质的静态单体函数和动量分布。结果涉及平均Fredholm行列式,我们进一步分析使用有效的形状因子的方法。用这种方法,我们得到的大距离行为的单体功能,它采取的形式的平均指数衰减。这种方法使我们能够研究一个实验上重要的制度的小动量的杂质的动量分布。我们还考虑了在短距离的单体函数和计算有限温度Tan的接触。

英文摘要:

We consider the McGuire model of a one-dimensional gas of free fermions interacting with a single impurity. We compute the static one-body function and momentum distribution of the impurity at finite temperatures. The results involve averages over Fredholm determinants that we further analyse using the effective form factors approach. With this approach, we derive the large-distance behaviour of the one-body function, which takes the form of an averaged exponential decay. This method allows us to study an experimentally important regime of small momenta of the impurity's momentum distribution. We also consider the one-body function at short distances and compute finite temperature Tan's contact.

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