A three-atom molecule AAB, formed by two identical bosons A and a distinct one B, is studied by considering coupled channels close to a Feshbach resonance. It is assumed that the subsystems AB and AA have, respectively, one and two channels, where, in this case, AA has open and closed channels separated by an energy gap. The induced three-body interaction appearing in the single channel description is derived using the Feshbach projection operators for the open and closed channels. An effective three-body interaction is revealed in the limit where the trap setup is tuned to vanishing scattering lengths. The corresponding homogeneous coupled Faddeev integral equations are derived in the unitarity limit. The s-wave transition matrix for the AA subsystem is obtained with a zero-range potential by a subtractive renormalization scheme with the introduction of two finite parameters, besides the energy gap. The effect of the coupling between the channels in the coupled equations is identified with the energy gap, which essentially provides an ultraviolet scale that competes with the van der Waals radius—this sets the short-range physics of the system in the open channel. The competition occurring at short distances exemplifies the violation of the “van der Waals universality” for narrow Feshbach resonances in cold atomic setups. In this sense, the active role of the energy gap drives the short-range three-body physics.

中文翻译：

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通用少原子系统中 N 体可调相互作用的出现

通过考虑接近费什巴赫共振的耦合通道，研究了由两个相同的玻色子 A 和不同的玻色子 B 形成的三原子分子 AAB。假设子系统 AB 和 AA 分别有一个和两个通道，在这种情况下，AA 具有由能隙隔开的开放和闭合通道。出现在单通道描述中的诱导三体相互作用是使用开放和封闭通道的 Feshbach 投影算子推导出来的。在陷阱设置被调整为消失的散射长度的极限中揭示了有效的三体相互作用。相应的齐次耦合 Faddeev 积分方程是在幺正性极限下推导出来的。AA 子系统的 s 波跃迁矩阵是通过减法重整化方案获得的零距离电位，除了能隙之外，还引入了两个有限参数。耦合方程中通道之间的耦合效应由能隙确定，它本质上提供了一个与范德华半径竞争的紫外线尺度——这设定了开放通道中系统的短程物理。在短距离内发生的竞争证明了冷原子设置中窄 Feshbach 共振违反了“范德瓦尔斯普遍性”。从这个意义上说，能隙的积极作用推动了短程三体物理。耦合方程中通道之间的耦合效应由能隙确定，它本质上提供了一个与范德华半径竞争的紫外线尺度——这设定了开放通道中系统的短程物理。在短距离内发生的竞争证明了冷原子设置中窄 Feshbach 共振违反了“范德瓦尔斯普遍性”。从这个意义上说，能隙的积极作用推动了短程三体物理。耦合方程中通道之间的耦合效应由能隙确定，它本质上提供了一个与范德华半径竞争的紫外线尺度——这设定了开放通道中系统的短程物理。在短距离内发生的竞争证明了冷原子设置中窄 Feshbach 共振违反了“范德瓦尔斯普遍性”。从这个意义上说，能隙的积极作用推动了短程三体物理。在短距离内发生的竞争证明了冷原子设置中窄 Feshbach 共振违反了“范德瓦尔斯普遍性”。从这个意义上说，能隙的积极作用推动了短程三体物理。在短距离内发生的竞争证明了冷原子设置中窄 Feshbach 共振违反了“范德瓦尔斯普遍性”。从这个意义上说，能隙的积极作用推动了短程三体物理。