Generalized quantum baker maps as perturbations of a simple kernel

Leonardo Ermann, Marcos Saraceno
2006 Physical Review E  
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 -
more » ... al properties - eigenvalues and eigenfunctions - of all the different quantizations.
doi:10.1103/physreve.74.046205 pmid:17155151 fatcat:m5dfsnn54jgi5kwb276k6nh4f4