Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems

This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems will be considered, those satisfying the classical Kolmogorov-Arnol'd-Moser scenario and those which not. The experimental realization of some of these systems using atom-optics methods will be mentioned.