We investigate the accuracy of Redfield theory predictions for the dynamics of a fully quantum-mechanical system-bath problem. Both the system and the bath in this model are harmonic oscillators, and the system is coupled linearly to the bath. This model can be solved exactly using well-known numerical techniques. We compare exact numerical calculations to the predictions of Redfield theory for a variety of coupling strengths. The expectation value of the system number operator and the system position autocorrelation function are the dynamical quantities we use in our comparisons. For those extreme cases in which Redfield theory does not exhibit good quantitative agreement, assumptions of Redfield theory are relaxed to obtain better approximations to the exact result.
Calculating the dynamical behavior for a quantum-mechanical many-body problem is inherently a difficult, if not impossible, task. One approach to this calculation which has been employed with substantial success is to separate the many-body problem into two parts [ 1-3 1. In this approach it is assumed that a small subset of the degrees of freedom in the problem can be considered the "system", and the remaining degrees of freedom represent the "bath". The division between system and bath is accomplished in a manner such that the degrees of freedom whose dynamics are of primary interest are contained in the system, and the remaining degrees of freedom, whose dynamics are of lesser interest, are contained in the bath. Physical examples which help to motivate this approach include time-resolved fluorescence experiments on solutes in dilute solution (see, for example, ref. [ 4]), vibrational and electronic population relaxation of adsorbates on surfaces (see, for example, ref. [ 5]), and vibrational/rotational energy transfer in molecule-surface collisions (see, for example, ref. [ 6]), In each of these cases, one molecule is considered the system, and the dynamics of