System-Reservoir Interactions

Abstract

The Weisskopf-Wigner theory of spontaneous emission of Chap. 14 is an example of a general class of problems involving the coupling of a small system to a large system. In that case the small system is the atom and the large system is the continuum of modes of the electromagnetic field. When computing the atomic decay rate, we were not interested in the field itself, but only on its effect on the atomic dynamics. Thus we never explicitly computed the field dynamics. Our theory leads to an irreversible decay of the upper state population. At first this should come as a surprise, since our starting equation (the Schrödinger equation) is reversible. Irreversibility results from two main approximations: 1) the assumption that the probability amplitude C _a0 (t) varies little during the time interval defined by the inverse bandwidth of the continuum of modes of the electromagnetic field, and 2) the replacement of the remaining nonlocal time integration in (14.58) by a δ-function. These choices comprise the Weisskopf-Wigner approximation.