Signatures of quantum mechanics in chaotic systems

TL;DR

This paper explores how chaotic classical systems can exhibit behaviors similar to quantum phenomena, such as entanglement, superposition, and measurement effects, challenging the notion that these are exclusive to quantum mechanics.

Contribution

It introduces the concept of chaotic entanglement via cupolets and discusses how classical chaotic systems can mimic quantum behaviors, broadening the understanding of quantum-classical correspondence.

Findings

Chaotic systems can support entanglement-like states called chaotic entanglement.

Disruption of chaotic entanglement resembles quantum decoherence.

Classical systems can exhibit analogs of wave function collapse and superposition.

Abstract

We consider 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 essentially highly-accurate stabilizations of its unstable periodic orbits. The 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 intervention. 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, then the chaotic entanglement would be broken. In this paper, we further describe chaotic entanglement and go on to discuss the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, the measurement problem, the superposition of states, and to quantum entropy definitions. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical.