质量不平衡三体系统在埃菲莫夫 - 非原子转变中的动量分布和接触参数
Momentum Distribution and Contact Parameters of a mass-imbalanced three-body system across the Efimov-Unatomic transition
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中文总结 AI 辅助
研究质量不平衡三体系统在临界维度\(D_c\)的动量分布与接触参数，发现\(D_c\)处渐近动量分布有独特对数标度结构，引入额外三体接触参数，分析中间区域，结果为探测少体量子系统尺度不变性转变提供实验特征。
中文摘要 AI 辅助
我们研究了在临界维度\(D_c\)下质量不平衡三体系统的单粒子动量分布和接触参数，在该维度下，随着空间维度在三维和二维之间调整，离散和连续尺度不变性之间发生转变。我们表明，\(D_c\)处的渐近动量分布由独特的对数标度结构控制，这与埃菲莫夫态的对数周期行为和非原子区域的幂律标度都有根本不同。这种结构需要引入一个与二次对数贡献相关的额外三体接触参数，从而在转变处对动量尾部进行有限且明确的描述。这个额外的三体参数敏感地依赖于质量不平衡，在不同质量配置下改变符号，对于相同粒子则消失。因此，三体对动量分布的贡献可以在一个特征动量尺度上被抑制，使得渐近尾部完全由两体接触决定。我们进一步分析了连接埃菲莫夫和非原子区域的狭窄中间区域，这里被确定为中间标度区域，其范围和性质受到质量比的强烈控制。这些结果将临界维度确立为具有涌现标度性质的区域，并为探测少体量子系统中离散和连续尺度不变性之间的转变提供了实验上可获取的特征。
英文摘要
We investigate the single-particle momentum distribution and contact parameters of mass-imbalanced three-body systems at the critical dimension Dc, where the transition between discrete and continuous scale invariance takes place as the spatial dimension is tuned between three and two dimensions. We show that the asymptotic momentum distribution at Dc is governed by a distinct logarithmic scaling structure, which differs fundamentally from both the log-periodic behavior of Efimov states and the power-law scaling of the unatomic regime. This structure requires the introduction of an additional three-body contact parameter associated with a quadratic logarithmic contribution, leading to a finite and well-defined description of the momentum tail at the transition. This additional three-body parameter depends sensitively on the mass imbalance, changing sign across different mass configurations and vanishing for identical particles. As a consequence, the three-body contribution to the momentum distribution can be suppressed at a characteristic momentum scale, leaving the asymptotic tail entirely determined by the two-body contact. We further analyze the narrow intermediate region connecting the Efimov and unatomic regimes, here identified as an intermediate scaling regime, whose extent and properties are strongly controlled by the mass ratio. These results establish the critical dimension as a regime with emergent scaling properties and provide experimentally accessible signatures for probing the transition between discrete and continuous scale invariance in few-body quantum systems.
