Quantum baker map on the sphere

Abstract

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.

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

References in corpus (5)

• Composed ensembles of random unitary matrices
• Using a quantum computer to investigate quantum chaos
• Overcoming the wall in the semiclassical baker's map
• Boundary contributions to the semiclassical traces of the baker's map
• A Canonical Quantization of the Baker's Map

Cited by in corpus (9)

• Entangling power of the quantum baker's map
• Quantum Iterated Function Systems
• Classical limit in terms of symbolic dynamics for the quantum baker's map
• Irreversible Quantum Baker Map
• The classical limit for a class of quantum baker's maps
• Decoherence and linear entropy increase in the quantum baker's map
• Quantization of Classical Maps with tunable Ruelle-Pollicott Resonances
• Quantum chaos in quantum dots coupled to bosons
• Different Traces of Quantum Systems Having the Same Classical Limit