混沌量子能级统计能用信息几何和推理方法来描述吗？
Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?
摘要：
在本文中，我们回顾了我们的新的信息几何动力学方法的混乱（IGAC）弯曲的统计流形，我们强调我们的信息几何动力学熵（IGE）作为一个指标的混乱在一个简单的应用程序的有用性。此外，知道可积和混沌量子反铁磁伊辛链的特点是渐近对数和线性增长的算子空间纠缠熵，分别，我们应用我们的IGAC提出了一个替代表征这样的系统。值得注意的是，我们表明，在前一种情况下，IGE表现出渐近对数增长，而在后一种情况下，IGE表现出渐近线性增长。在其发展的这个阶段，IGAC仍然是一个雄心勃勃的统一的信息几何理论结构的混沌动力学研究与几个未解决的问题。然而，根据我们最近的发现，我们相信它可以提供一个有趣的，创新的和潜在的强大的方式来研究和理解经典和量子混沌的非常重要和具有挑战性的问题。
英文摘要：
In this paper, we review our novel information geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy (IGE) as an indicator of chaoticity in a simple application. Furthermore, knowing that integrable and chaotic quantum antiferromagnetic Ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies, respectively, we apply our IGAC to present an alternative characterization of such systems. Remarkably, we show that in the former case the IGE exhibits asymptotic logarithmic growth while in the latter case the IGE exhibits asymptotic linear growth. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it could provide an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.
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