Exact Derivation of a Generalized Master Equation for the Motion of Excitons

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Abstract
Starting from the Nakajima‐Zwanzig equation, by an exact evaluation of its kernel, a generalized master equation, describing the coherent motion of excitons is derived. The time dependence of the kernel is discussed in detail. From this coupled set of integro‐differential equations a set of second order differential equations is obtained. In the continuum approximation, this set results in a partial differential equation in space and time variables, which only for large times assumes the form of a wave equation. Explicit solutions of the various equations of motion are presented and discussed.