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Signatures of Quantum Mechanics in Chaotic Systems
Kevin M Short1, Matthew A Morena2
1Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Chaotic systems can exhibit quantum-like behaviors, such as chaotic entanglement, challenging the exclusive quantum nature of these phenomena. This research explores quantum-classical correspondence through classical chaotic dynamics.
Area of Science:
- Complex Systems
- Quantum Mechanics
- Classical Dynamics
Background:
- Investigating the quantum-classical correspondence from a classical viewpoint.
- Exploring behaviors typically associated with quantum mechanics in classical chaotic systems.
Purpose of the Study:
- To analyze the potential for chaotic systems to exhibit quantum-like phenomena.
- To describe chaotic entanglement and its properties analogous to quantum entanglement.
- To examine analogs of wave function collapse, entropy, superposition, and the measurement problem in chaotic systems.
Main Methods:
- Utilizing a chaotic system's set of cupolets (stabilized unstable periodic orbits) as the primary analytical tool.
- Observing and analyzing bound or entangled states between interacting chaotic systems.
- Investigating the behavior of cupolets in mutually-sustaining stabilization states.
Main Results:
- Detection of bound or entangled states between interacting chaotic systems, termed chaotic entanglement.
- Demonstration that chaotic entanglement exhibits properties consistent with quantum entanglement, such as breaking upon disturbance.
- Identification of classical analogs for wave function collapse, entropy, superposition, and the measurement problem within chaotic systems.
Conclusions:
- Quantum mechanical characteristics may not be exclusively quantum in nature.
- Chaotic systems can exhibit behaviors conventionally attributed to quantum mechanics.
- While exhibiting analogs, quantum entanglement possesses unique characteristics not fully replicated by chaotic entanglement.
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