开放系统中的共振链、广义Zeta函数和长度谱的聚类
Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum
摘要：
在物理学和数学中的许多不可积的开放系统中，共振已经被发现沿着复平面中的曲线令人惊讶地有序。在这篇文章中，我们提供了一个统一的方法，这些共振链广义动态zeta函数。通过一个详细的数值研究，我们表明，这些广义zeta函数解释的机制，创建链的量子共振和经典Ruelle共振3盘系统以及几何共振肖特基表面。我们还提出了一个直接的系统内禀定义的连续线上的共振串在一起作为一个分析品种的投影。此外，这种方法表明，共振链的存在是直接相关的集群的经典长度谱的倍数的基础长度。最后，这个链接是用来构建新的例子，几种不同的结构的共振链共存。
英文摘要：
In many non-integrable open systems in physics and mathematics resonances have been found to be surprisingly ordered along curved lines in the complex plane. In this article we provide a unifying approach to these resonance chains by generalizing dynamical zeta functions. By means of a detailed numerical study we show that these generalized zeta functions explain the mechanism that creates the chains of quantum resonance and classical Ruelle resonances for 3-disk systems as well as geometric resonances on Schottky surfaces. We also present a direct system-intrinsic definition of the continuous lines on which the resonances are strung together as a projection of an analytic variety. Additionally, this approach shows that the existence of resonance chains is directly related to a clustering of the classical length spectrum on multiples of a base length. Finally, this link is used to construct new examples where several different structures of resonance chains coexist.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
