Mur-Petit Jordi, Molina Rafael A
Instituto de Estructura de la Materia, IEM-CSIC, Serrano 123, 28006 Madrid, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042906. doi: 10.1103/PhysRevE.92.042906. Epub 2015 Oct 5.
We perform a comprehensive analysis of the spectral statistics of the molecular resonances in (166)Er and (168)Er observed in recent ultracold collision experiments [Frisch et al., Nature (London) 507, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until B∼30 G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a 20%-25% fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.
我们对近期在超冷碰撞实验[弗里施等人，《自然》（伦敦）507, 475 (2014)]中观测到的(166)Er和(168)Er分子共振的光谱统计进行了全面分析，目的是确定该系统的混沌性。我们计算了不同的独立统计特性，以检查它们与随机矩阵理论（RMT）的一致程度，并分析它们是否与存在缺失共振的可能性相一致。作为磁场函数的短程涨落分析表明，直到B∼30 G时混沌性持续增加。对于更高的磁场，排斥参数减小，这种效应可解释为由于存在缺失共振。长程涨落分析使我们能够更定量地估计缺失能级的比例为20% - 25%。最后，对共振宽度分布的研究提供了额外证据，支持与实验磁场分辨率相比小宽度的缺失共振。我们得出结论，需要进行更高分辨率的进一步测量，才能最终回答缺失共振问题以及与RMT的一致性问题。
