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

References in corpus (3)

• Entangling power of the quantum baker's map
• The classical limit for a class of quantum baker's maps
• Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

Cited by in corpus (3)

• Multifractality and intermediate statistics in quantum maps
• On the resonance eigenstates of an open quantum baker map
• Transport phenomena in the asymmetric quantum multibaker map