Signatures of chaos in periodically driven quantum systems

One-dimensional, time-periodic systems are the simplest systems that can exhibit classical chaos. The quantum versions of these systems are ideal for investigations of how classical chaos affects quantum dynamics. These systems are also relevant to recent experiments involving high-intensity, pulsed lasers. In this dissertation, we investigate open and closed quantum systems driven by a periodic field. We examine the phase-space structure of the Floquet eigenstates of these systems to determine their relationship to classical phase-space structures. We observe the effects of classical dynamics on the radiation spectra of these Floquet states and their superpositions. We show how avoided crossings can lead to delocalization of the Floquet states and illustrate how certain features of the classical motion can prevent this delocalization. We show how resonance states in an open system are related to periodic orbits of the classical motion and how this relationship causes the number of resonance states in one system to increase as the driving field is increased. We examine how the phase-space structure of resonance states changes as they are destroyed by coupling to the continuum and as they pass through an avoided crossing. We also present a unified picture of the evolution of a closed quantum system as its classical counterpart becomes chaotic and we point out that modification of this picture is necessary to account for the phenomena observed in open systems.