泄漏混沌系统
Leaking Chaotic Systems
摘要：
有许多物理情况下，一个洞或泄漏被引入一个否则封闭的混沌系统。泄漏可以有一个自然的起源，它可以模仿测量设备，它也可以用来揭示封闭系统的动态特性。在本文中，我们提供了一个统一的处理泄漏系统，我们审查应用程序不同的物理问题，无论是在经典和量子图片。我们的治疗是基于开放系统的瞬态混沌理论，这是必不可少的，因为真正的泄漏有有限的大小，因此估计的基础上的封闭系统从本质上不同于观察。审查的应用领域非常广泛，从行星天文学和流体力学流动，到等离子体物理和量子保真度。该理论的扩展和适应的情况下，部分泄漏（部分吸收/传输）与应用程序的房间声学和光学微腔。在台球的lima .con家族中的模拟说明了正文。关于台球动力学，我们强调，一个正确的离散时间表示只能在所谓的真实时间映射，而传统的庞加莱映射导致错误的结果。我们推广Perron-Frobenius型运营商，使他们描述的实时部分泄漏的地图。
英文摘要：
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. In this paper we provide an unified treatment of leaking systems and we review applications to different physical problems, both in the classical and quantum pictures. Our treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows, to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption/transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the lima .con family of billiards illustrate the main text. Regarding billiard dynamics, we emphasize that a correct discrete time representation can only be given in terms of the so- called true-time maps, while traditional Poincar é maps lead to erroneous results. We generalize Perron-Frobenius-type operators so that they describe true-time maps with partial leaks.
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