Quantized chaotic dynamics and non-commutative KS entropy
- Department of Mathematics, Indiana University-Purdue University at Indianapolis, Indianapolis, Indiana 46205 (United States)
- Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138 (United States)
We study the quantization of two examples of classically chaotic dynamics, the Anosov dynamics of {open_quote}{open_quote}cat maps{close_quote}{close_quote} on a two dimensional torus, and the dynamics of baker{close_quote}s maps. Each of these dynamics is implemented as a discrete group of automorphisms of a von Neumann algebra of functions on a quantized torus. We compute the non-commutative generalization of the Kolmogorov-Sinai entropy, namely the Connes-Sto/rmer entropy, of the generator of this group, and find that its value is equal to the classical value. This can be interpreted as a sign of persistence of chaotic behavior in a dynamical system under quantization. Copyright {copyright} 1996 Academic Press, Inc.
- OSTI ID:
- 383081
- Journal Information:
- Annals of Physics (New York), Vol. 248, Issue 2; Other Information: PBD: Jun 1996
- Country of Publication:
- United States
- Language:
- English
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