发表机构
Universidad Mayor; Universidade Federal de Pernambuco（市长大学; 伯南布哥联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过多尺度谱统计方法分析超冷铒原子碰撞的共振谱，发现中间量子混沌特征，提出半泊松统计与尺度依赖的谱刚度损失，为理解混合相空间混沌提供新视角。
AI 中文摘要
表征具有混合相空间的系统中的中间量子混沌需要探测跨多个尺度的谱相关性。在此，我们利用高阶间距比、间距增量以及抽取水平序列的累积功率谱密度，对超冷166Er和168Er原子的共振谱进行了多尺度统计分析。我们的分析揭示，虽然谱表现出清晰的能级排斥，但它们始终比标准Wigner-Dyson系综更好地由半泊松分布描述，且这种中间特性在高阶相关性中持续存在。累积功率谱揭示了一个中间的1/f^alpha区域，在全谱分辨率下alpha约为1.5，在中间抽取尺度下趋向于可积随机游走极限alpha=2，表明谱刚度的尺度依赖性损失。此外，间距增量分布独立地揭示了介于拉普拉斯和高斯极限之间的统计特性。综合这些互补的诊断，表明半泊松特性反映了超越最近邻尺度的持久非Wigner-Dyson相关性，为中间量子混沌提供了一致的图景，并可能与底层碰撞动力学中的分层捕获有关。
英文摘要
Characterizing intermediate quantum chaos in systems with mixed phase spaces requires probing spectral correlations across multiple scales. Here, we present a multi-scale statistical analysis of the resonance spectra of ultracold 166Er and 168Er atoms using higher-order spacing ratios, spacing increments, and the accumulated power spectral density of decimated level sequences. Our analysis reveals that while the spectra exhibit clear level repulsion, they are consistently better described by semi-Poisson than by standard Wigner-Dyson ensembles, with this intermediate character persisting across higher-order correlations. The accumulated power spectrum reveals an intermediate 1/f^alpha regime, with alpha approximately 1.5 at full spectral resolution and a tendency toward the integrable random-walk limit alpha = 2 at intermediate decimation scales, indicating a scale-dependent loss of spectral rigidity. Furthermore, the spacing-increment distributions independently reveal statistics intermediate between Laplace and Gaussian limits. Together, these complementary diagnostics show that the semi-Poisson character reflects persistent non-Wigner-Dyson correlations beyond the nearest-neighbor scale, providing a consistent picture of intermediate quantum chaos and a possible connection to hierarchical trapping in the underlying collision dynamics.
