QUANTUM MAPS WITH SPACE EXTENT: A PARADIGM FOR LATTICE QUANTUM WALKS

Classical multibaker maps are deterministic models of classical random walks. Quantum multibaker maps are their quantum versions. As such, they can be naturally considered quantum random walks. In this review we discuss the construction and properties of quantum multibaker maps and related, more general models, in the context of the recent results in dynamical systems approach to nonequilibrium statistical mechanics. Properties of other models of quantum walks are also discussed.