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Signatures of Quantum Mechanics in Chaotic Systems

1
Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA
2
Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(6), 618; https://doi.org/10.3390/e21060618
Received: 6 May 2019 / Revised: 14 June 2019 / Accepted: 19 June 2019 / Published: 22 June 2019
(This article belongs to the Special Issue Quantum Chaos and Complexity)
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Abstract

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. View Full-Text
Keywords: quantum entanglement; chaotic entanglement; chaotic systems; cupolets; entropy; correspondence; unstable periodic orbits quantum entanglement; chaotic entanglement; chaotic systems; cupolets; entropy; correspondence; unstable periodic orbits
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Short, K.M.; Morena, M.A. Signatures of Quantum Mechanics in Chaotic Systems. Entropy 2019, 21, 618.

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