Generalized Quantum Baker Maps as perturbations of a simple kernel

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.

11 pages, 17 figures

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Cited by in corpus (7)

• Multifractality and intermediate statistics in quantum maps
• On the resonance eigenstates of an open quantum baker map
• Classical transients and the support of open quantum maps
• Transient features of quantum open maps
• The modular multiplication operator and the quantized bakers maps
• Transport phenomena in the asymmetric quantum multibaker map
• Chaotic Roots of the Modular Multiplication Dynamical System in Shor's Algorithm