Short Kevin M, Morena Matthew A
Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA.
Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA.
Entropy (Basel). 2019 Jun 22;21(6):618. doi: 10.3390/e21060618.
We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system's set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique.
我们从经典视角审视量子 - 经典对应关系，探讨混沌系统支持通常与量子力学系统相关行为的可能性。我们主要的分析工具是混沌系统的一组杯状体，它们是其不稳定周期轨道的高精度稳定化。我们的讨论源于我们最近在相互作用的混沌系统之间检测到的束缚或纠缠态，其中成对的杯状体被诱导进入一种相互维持稳定的状态，这种状态无需外部控制就能维持。这种状态被称为混沌纠缠，因为它已被证明表现出与量子纠缠一致的若干特性。例如，如果相互作用受到干扰，混沌纠缠就会被打破。在本文中，我们进一步描述混沌纠缠，并继续探讨混沌系统展现其他传统上与量子力学相关特征的能力，即类似于波函数坍缩、各种熵的定义、态的叠加以及测量问题。在此过程中，我们认为这些特征不必仅被视为量子力学所特有的。我们还讨论了量子系统的几个与混沌纠缠不完全兼容且使量子纠缠独一无二的特征。
