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arXiv 2103.08772cond-mat.quant-gasphysics.atom-ph
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一维玻色气体中极化子间的介导相互作用

Mediated interaction between polarons in a one-dimensional Bose gas

Aleksandra Petkovic, Zoran Ristivojevic

摘要:

本文研究了具有两个与玻色子密度局部耦合的杂质的弱相互作用一维玻色气体。我们推导出任意耦合和分离$r$的杂质之间的诱导相互作用的分析结果。在$r\lesssim ξ$,其中$ξ$表示玻色气体的愈合长度,相互作用很好地描述了平均场的贡献。它的形式变化的耦合增加,接近$r$的线性函数在短距离的强耦合制度。对于$r\ggξ$,平均场贡献在任意耦合下呈指数衰减。然而,在如此长的距离上,量子涨落的影响变得很重要,对诱导的相互作用产生了长距离的量子贡献。在最长距离下,它表现为$1/r^3$,而在强耦合下,我们发现具有较慢衰减的中间距离区域,$1/r$。还计算了交叉区的量子贡献。杂质之间的诱导相互作用(即,极化子)是有吸引力的,并导致形成它们的束缚态,称为双极化子。我们讨论它的结合能。

英文摘要:

We study a weakly-interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary coupling and separation $r$. At $r\lesssim ξ$, where $ξ$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of $r$ at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\ggξ$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as $1/r^3$, while at strong coupling we find an intermediate distance regime with a slower decay, $1/r$. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.

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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