Quantum electrodynamics of resonant energy transfer in condensed matter. II. Dynamical aspects

A microscopic quantum electrodynamical (QED) theory is developed for representing the dynamics of excitation transfer in a dielectric medium between individual species, such as atoms or molecules, at various separations, including both near- and far-zone distances. The theory, built on explicit QED consideration of the time evolution, fully incorporates medium-induced energy renormalizations and damping corrections for the transfer species. In addition, it embodies the local field and screening contributions which have already been featured in a previous paper devoted to the rate description. The influence of the medium is also manifest in the relativistic time-lag (reflecting the delay of the initial arrival of the excitation at the acceptor molecule), which is now shown to be characterized by the group velocity of the light. The phase velocity features in the distance-dependent retardation in phase of the transition matrix element. The theory extends to different transfer regimes. Following a general analysis, the paper reexamines the rate regime, where not only the transition matrix element but also the molecular excitation frequencies for the transfer species are modified by the medium. Another non-rate-regime, occurring in situations that lack an intrinsic molecular density of states, displays oscillatory dynamics over short transfer distances. These oscillations are suppressed by monomolecular damping in the long-range case: here the transfer process is cast in terms of transfer probabilities, rather than rates. In all situations the characteristic parameters of the process properly reflect the influence of the medium, though it is apparent that in the limiting case of an infinitely dilute medium the present results are consistent with those previously obtained for the vacuum case.