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From Chaos & Strange Attractors to Quantum Theory

Ervin Goldfain

Published Mar 1, 2020• 0 citations
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Abstract

An open debate exists nowadays on how to properly connect chaos theory and strange attractors, on the one hand, to Quantum Field Theory (QFT) and Quantum Mechanics (QM) on the other. We post here a condensed flow-chart reflecting our personal view on this connection.

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An open debate exists nowadays on how to properly connect chaos theory and strange attractors, on the one hand, to Quantum Field Theory (QFT) and Quantum Mechanics (QM) on the other. We post here a condensed flow-chart reflecting our personal view on this topic.

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Κβαντικά χαοτικά συστήµατα

Κωνσταντίνος Ζαχαρίου, Αλέξανδρος Μαρτινέγκος

Our work is divided into 6 parts. The first part is the chaos theory. An introduction to a mathematical world and some of the biggest and most famous experiments. Some of them are the attractors, the three-body problem and the Principle of Uncertainty. The second part is the Quantum Physics or Quantum Mechanics. Large theories that changed the way we think and the way we perceive the universe as many of the greatest physicists who have passed from this world, are referred to this part. The third part, and the shortest is the Quantum Chaos. A part of physics, that studies how a quantum system behaves, whose classical limit is Chaotic. In simpler words, the attempt to connect quantum physics and chaos. The fourth part includes some biographical information of the greatest scientists. The fifth and sixth part, are some explanations and our sources.

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Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and quantum mechanics. It challenges the received view that classical and quantum mechanics are incommensurable, and revives another, largely forgotten tradition due to Niels Bohr and Paul Dirac. By artfully weaving together considerations from the history of science, philosophy of science, and contemporary physics, this book offers a new way of thinking about intertheory relations and scientific explanation. It will be of particular interest to historians and philosophers of science, philosophically-inclined physicists, and interested non-specialists.
Our work is divided into 6 parts. The first part is the chaos theory. An introduction to a mathematical world and some of the biggest and most famous experiments. Some of them are the attractors, the three-body problem and the Principle of Uncertainty. The second part is the Quantum Physics or Quantum Mechanics. Large theories that changed the way we think and the way we perceive the universe as many of the greatest physicists who have passed from this world, are referred to this part. The third part, and the shortest is the Quantum Chaos. A part of physics, that studies how a quantum system behaves, whose classical limit is Chaotic. In simpler words, the attempt to connect quantum physics and chaos. The fourth part includes some biographical information of the greatest scientists. The fifth and sixth part, are some explanations and our sources.
Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and quantum mechanics. It challenges the received view that classical and quantum mechanics are incommensurable, and revives another, largely forgotten tradition due to Niels Bohr and Paul Dirac. By artfully weaving together considerations from the history of science, philosophy of science, and contemporary physics, this book offers a new way of thinking about intertheory relations and scientific explanation. It will be of particular interest to historians and philosophers of science, philosophically-inclined physicists, and interested non-specialists.
We investigate the connection between classical and quantum chaos in a dissipative system of two coupled collective spins. Although the classical dynamics possesses a stable fixed-point attractor, we find pronounced signatures of chaos in the transient dynamics preceding relaxation. In the quantum model, such transient chaos is accompanied by a transition to random-matrix statistics in the relevant part of the Liouvillian spectrum and by a qualitative increase in the number of Liouvillian modes contributing to expectation values of physical observables. The transition occurs before the bifurcation at which the stable fixed point disappears and a chaotic attractor emerges. Our results show that Liouvillian quantum chaos can be associated with transient classical chaos, rather than requiring a chaotic asymptotic attractor, and provide a refinement of the Grobe-Haake-Sommers conjecture.