Relations of Memories to Other Entities and GME Solutions for the Linear Chain

Abstract

Relations of the memory function (GME) theory of exciton transport to other theories and entities in statistical mechanics and condensed matter, as well as solutions of the GME theory for a specific system of special interest to experiments, the linear chain, were the content of this chapter. Our theory is built as a generalization of the theories of Forster as well as Dexter but looks quite different from those developed by Haken and Reineker, and by Grover and Silbey. It was shown that the approaches can be unified by establishing relations among them by inspecting them all in terms of memory functions. Their conceptual differences from the GME theory were also analyzed. It was argued that each method has its own particular purpose and use, separate from the others. The connection between memory functions in probability equations and correlation functions encountered more usually in statistical mechanics within the framework of linear response was analyzed. The two examples selected for this comparison were velocity correlation functions used in mobility or conductivity theory, (Kubo 1957), and scattering functions used in neutron diffraction (Van Hove 1954b). Respectively, they find application in charge mobility physics and in the study of the movement of hydrogen atoms and other interstitials in metals. The next content of the chapter was explicit solutions of the GME extended to have the simple Wigner-Weisskopf incorporation of incoherence in them. These solutions will be useful in subsequent chapters where the effect of coherence is studied on transient grating, Ronchi ruling, and sensitized luminescence observations. Solutions for the full SLE case (with hopping terms added) were also provided. Finally in this chapter, partially nonlocal memories and transfer rates were shown to arise from strong intersite coupling. This chapter thus connects memory functions, primary to the book, to more familiar entities in statistical mechanics and condensed matter physics.