  The dynamics of an electronic two-level system coupled to an electromagnetic
field are simulated explicitly for one and three dimensional systems through
semiclassical propagation of the Maxwell-Liouville equations. We consider three
flavors of mixed quantum-classical dynamics: the classical path approximation
(CPA), Ehrenfest dynamics, and symmetrical quantum-classical (SQC) dynamics.
The CPA fails to recover a consistent description of spontaneous emission. A
consistent "spontaneous" emission can be obtained from Ehrenfest
dynamics--provided that one starts in an electronic superposition state.
Spontaneous emission is always obtained using SQC dynamics. Using the SQC and
Ehrenfest frameworks, we further calculate the dynamics following an incoming
pulse, but here we find very different responses: SQC and Ehrenfest dynamics
deviate sometimes strongly in the calculated rate of decay of the transient
excited state. Nevertheless, our work confirms the earlier observations by W.
Miller [J. Chem. Phys. 69, 2188-2195, 1978] that Ehrenfest dynamics can
effectively describe some aspects of spontaneous emission and highlights new
possibilities for studying light-matter interactions with semiclassical
mechanics.
