Quantum baker map on the sphere

Details Quantum baker map on the sphere Quantum baker map on the sphere

1998-05-23

arxiv.org/abs/chao-dyn/9805020v2

Nonlinearity 12 (1999) 269-284

Nonlinear Sciences

Chaotic Dynamics

REVTeX 15 pages, 6 figures included (ps format), final published version with generalizetion of the model

Scientific paper

10.1088/0951-7715/12/2/007

We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct and investigate a family of the corresponding quantum maps. In the simplest case of the model the system does not possess a time reversal symmetry and the quantum map is represented by real, orthogonal matrices of even dimension. The semiclassical ensemble of quantum maps, obtained by averaging over a range of matrix sizes, displays statistical properties characteristic of circular unitary ensemble. Time evolution of such systems may be studied with the help of the SU(2) coherent states and the generalized Husimi distribution.

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