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Chaos in a Model of an Open Quantum System

Published online by Cambridge University Press:  01 April 2022

Frederick M. Kronz
Frederick M. Kronz*
Affiliation:
The University of Texas at Austin
*
†Send requests for reprints to the author, Department of Philosophy, The University of Texas at Austin, Austin, TX 78712; email: kronz@mail.utexas.edu.
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Abstract

In a previous essay I argued that quantum chaos cannot be exhibited in models of quantum systems within von Neumann's mathematical framework for quantum mechanics, and that it can be exhibited in models within Dirac's formal framework. In this essay, the negative thesis concerning von Neumann's framework is elaborated further by extending it to the case of Hamiltonian operators having a continuous spectrum. The positive thesis concerning Dirac's formal framework is also elaborated further by constructing a chaotic model of an open quantum system in which an entropy measure is shown to approach its maximum value as time goes to infinity. Having such an entropy measure is a characteristic that is closely connected to chaotic behavior in phase space models of classical systems.

Type
Philosophy of Physics and Chemistry
Information
Philosophy of Science , Volume 67 , Issue S3: Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part II: Symposia Papers Sep., 2000 , 2000 , pp. S446 - S453
Copyright
Copyright © 2000 by the Philosophy of Science Association

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Footnotes

‡

This essay was completed with support from the National Science Foundation, grant number SBR-9602122. I would like to thank Charles Radin for his expert assistance with some of the technical issues involved in the second section of this essay having to do with the spectral representation of bounded and unbounded operators in an infinite-dimensional separable Hilbert space.

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