通用窗口内对$N$玻色子系统的次级贡献
Subleading contributions to $N$-boson systems inside the universal window
摘要：
我们研究玻色子系统中的制度，在该制度中的两体系统具有浅的束缚态，或者等价地，一个大的值的两体散射长度。以有效场论为指导，我们构造了一系列势项，这些势项在描述系统的结合能时具有递减的重要性。主导阶势项由两体项（通常是吸引力）和三体项（通常是排斥力）组成;最后一项是防止具有两个以上粒子的系统崩溃所必需的。在这个顺序下，两体势的参数化是为了获得散射长度的正确描述，散射长度决定了这个区域的动力学，而三体项则固定了三体数据。我们调查的作用，切断在领导秩序的描述，我们扩展了探索超越领导秩序，包括下一个领导秩序的条款，两个和三体的潜力。我们使用的N体系统，其能量是变分估计的稳定性的要求，引入三体力。潜在的参数化，作为一个功能的截止，是固定的，以描述能量的4个He团簇高达7个粒子在预期的精度。最后，我们还探讨了同时描述原子-二聚体散射长度的可能性。
英文摘要：
We study bosonic systems in the regime in which the two-body system has a shallow bound state or, equivalently, a large value of the two-body scattering length. Using the effective field theory framework as a guide, we construct a series of potential terms which have decreasing importance in the description of the binding energy of the systems. The leading order potential terms consist of a two-body term, usually attractive, plus a three-body term, usually repulsive; this last term is required to prevent the collapse of systems with more than two particles. At this order, the parametrization of the two-body potential is done to obtain a correct description of the scattering length, which governs the dynamics in this regime, whereas the three-body term fixes a three-body datum. We investigate the role of the cut-off in the leading order description and we extend the exploration beyond the leading order by including the next-to-leading order terms in both, the two- and three-body potentials. We use the requirement of the stability of the N-body system, whose energy is variationally estimated, to introduce the three-body forces. The potential parametrization, as a function of the cut-off, is fixed to describe the energy of 4 He clusters up to seven particles within the expected accuracy. Finally, we also explore the possibility to describe at the same time the atom-dimer scattering length.
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