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Quantization of Anosov Maps

✍ Scribed by M.B. Dematos; A.M.O. Dealmeida

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 745 KB
Volume: 237
Category: Article
ISSN: 0003-4916
DOI: 10.1006/aphy.1995.1003

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✦ Synopsis

Cat maps, linear automorphisms of the torus, are standard examples of classically chaotic systems, but they are periodic when quantized, leading to many untypical consequences. Anosov maps are topologically equivalent to cat maps despite being nonlinear. Generalizing the original quantization of cat maps, we establish that quantum Anosov maps have typical spectral fluctuations for classically chaotic systems. The periodic orbit theory for the spectra of quantum Anosov maps is not exact, as it is for cat maps. Nonetheless our calculations verify that the semiclassical trace of the propagator is accurate well beyond any "log time" cutoff. 1995 Academic Press, Inc.

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