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Generalized Quantum Baker Maps as perturbations of a simple kernel

Leonardo Ermann·Marcos Saraceno
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Abstract

We present a broad family of quantum baker maps that generalize the proposal of Schack and Caves to any even Hilbert space with arbitrary boundary conditions. We identify a structure, common to all maps consisting of a simple kernel perturbed by diffraction effects. This "essential" baker's map has a different semiclassical limit and can be diagonalized analytically for Hilbert spaces spanned by qubits. In all cases this kernel provides an accurate approximation to the spectral properties - eigenvalues and eigenfunctions - of all the different quantizations.

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Leonardo Ermann, Marcos Saraceno. 2006-07-21. Generalized Quantum Baker Maps as perturbations of a simple kernel. https://doi.org/10.1103/physreve.74.046205

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