On the Quantum Cat and Sawtooth Maps- Return to Generic Behaviour

Details On the Quantum Cat and Sawtooth Maps- Return to Generic Behaviour On the Quantum Cat and Sawtooth Maps- Return to Generic Behaviour

1993-07-12

arxiv.org/abs/chao-dyn/9307005v1

Nonlinear Sciences

Chaotic Dynamics

10 pages LaTex. 6 figures not included. Please send for PostScript files to first author at the e-mail address

Scientific paper

The quantization of the continous cat maps on the torus has led to rather pathological quantum objects [6]. The non-generic behaviour of this model has led some to conclude that the Correspondence Principle fails in this case [2]. In this note we introduce the quantum sawtooth models, since this is the natural family to which the cat maps belong. Thus, a simple propagator depending on a parameter is constructed which for integer values of the parameter becomes pathological quantum cat maps, while away from integer values we find a return to the generic behaviour of non-integrable quantum systems.

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