Quantum kicked rotor and its variants: Chaos, localization and beyond

Kicked rotor is a paradigmatic model for classical and quantum chaos in time-dependent Hamiltonian systems. More than fifty years since the introduction of this model, there is an increase in the number of works that use kicked rotor model as a fundamental template to study a variety of questions in nonlinear dynamics, quantum chaos, condensed matter physics and quantum information. This is aided by the experimental approaches that have implemented many variants of the quantum kicked rotor model. The problems addressed using kicked rotor and its variants include the basic phenomenology of classical and quantum chaos, transport and localization in one- and higher dimensional kicked systems, effects of disorder and interactions, resonant dynamics and the relation between quantum correlations and chaos. This would also include a range of applications such as for constructing ratchet dynamics and for atom-optics based interferometry. This article reviews the current status of theoretical and experimental research devoted to exploring these ideas using the framework of kicked rotor model.