Quantized chaotic dynamics and non-commutative KS entropy

Journal Article · Sat Jun 01 04:00:00 EDT 1996 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1996.0056· OSTI ID:383081

Klimek, S ^[1]; Lesniewski, A ^[2]

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1. Department of Mathematics, Indiana University-Purdue University at Indianapolis, Indianapolis, Indiana 46205 (United States)
2. 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), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 248; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHAOTIC SYSTEMS
DYNAMICS
ENTROPY
ERGODIC HYPOTHESIS
MAPPING
QUANTIZATION
TORI