Relations among theories of excitation transfer

Abstract

A study of the formal relations existing among three recent theories of excitation transfer is made and exact results concerning the two-molecule system are presented. An equivalence is established between the Haken-Reineker-Strobl (HRS) and the Grover-Silbey (GS) formalisms (before the partial Markoffian approximation) on one hand and the Kenkre-Knox (KK) formalism on the other. This equivalence takes the form of a simple relation between the KK memory $\mathcal{W}\mathrm{}\left(t\right)\mathrm{}$ and a function [$g\left(t\right)-1\mathrm{}$] appearing in the GS theory. It is shown that the two-term nature of the GSHRS diffusion constant can be understood clearly in terms of this relation, and the ranges of validity of the various theories, including that of the "GSHRS equation," are discussed.