Nonexponential decay in relaxation phenomena and the spectral characteristics of the heat bath

After a brief survey of the characteristics of a heat bath and its role in relaxation phenomena leading to the familiar exponential decay, it is argued that the nonexponential form found commonly in many condensed matter systems indicates that the energy spectrum of the heat bath plays a crucial part in these phenomena. In equilibrium statistical mechanics, the mean energy of a heat bath determines the temperature of a system placed in contact with it. We show that the relaxation of a system placed in contact with this heat bath is determined by the distribution of the energy level spacings for level spacings small as compared to the mean spacing. After presenting arguments in favor of a linear behavior of this distribution, we show, in a somewhat heuristic way, that the resulting relaxation function has a nonexponential form.