The photon field dynamics of a single non-decaying mode of a quantized electromagnetic field in a binomial state interacting with a three-level system is studied non-perturbatively. It is found that the phenomenon of collapse and revival is not only sensitive to the initial photon statistics, but also to photon density, coupling constants and detunings.

By coupling a kicked quantum system to a bath of harmonic oscillators we derive a logistic map with quantum corrections. We find a period-doubling route to the classical behavior as a dissipation parameter is increased, and other interesting features at intermediate values of this parameter.

The problem of quantum chaos is to understand how, if at all, classical notions of chaos carry over into quantum theory. Classically, chaos is defined as the property of very sensitive dependence on initial conditions. More precisely, a system is defined to be chaotic if at least one of its Lyapunov characteristic exponents (LCE) is positive. [1] Quantum systems never seem to have positive LCE: the wave function evolves in time in a more orderly fashion than the chaotic trajectories of the corresponding classical system.

We calculate the vacuum-field radiation pressure on two parallel, perfectly conducting plates. The modes outside the plates push the plates together, those confined between the plates push them apart, and the net effect is the well-known Casimir force. Implications of this result for the form of the Poynting vector in quantum electrodynamics are discussed.

We compare the classical and quantum theories of a Morse oscillator driven by a sinusoidal field, focusing attention on multiple-photon excitation and dissociation. In both the classical and quantum theories the threshold field strength for dissociation may be estimated fairly accurately on the basis of classical resonance overlap, and the classical and quantum results for the threshold are in good agreement except near higher-order classical resonances and quantum multiphoton resonances. We discuss the possibility of ``quantum chaos'' in such driven molecular systems and use the Morse oscillator to test the manifestations of classical resonance overlap suggested semiclassically.

We extend our previous comparison of classical and quantum theories for the excitation and dissociation of a sinusoidally driven Morse oscillator [Phys. Rev. A 37, 796 (1988)] to the case of two-frequency driving. In both the classical and quantum theories the total threshold intensity for dissociation can be considerably smaller in the two-frequency case. This is consistent with results obtained with more artificial models of laser-driven molecular systems, and we provide an approximate resonance-overlap analysis to explain this trend. We also compare results obtained with adiabatic and sudden turn-on of the applied field, and comment on the use of absorbing boundaries for the computational identification of dissociation or ionization.

We consider a two-state system kicked quasiperiodically by an external force. When the two kicking frequencies assumed for the force are incommensurate, there can be quantum chaos in the sense that (a) the autocorrelation function of the state vector decays, (b) the power spectrum of the state vector is broadband, and (c) the motion on the Bloch sphere is ergodic. The time evolution of the state vector is nevertheless dynamically stable in the sense that memory of the initial state is retained. We also consider briefly the kicked quantum rotator and find, in agreement with Shepelyansky [Physica 8D, 208 (1983)], that the quantum localization effect is greatly weakened by the presence of two incommensurate driving frequencies.