Deviation from exponential law and Van Hove's “lambda^2 t” limit

The deviations from a purely exponential behavior in a decay process are analyzed in relation to Van Hove’s “lambda^2 t” limiting procedure. Our attention is focused on the effects that arise when the coupling constant is small but nonvanishing. We first consider a simple model (two-level atom in interaction with the electromagnetic field), then gradually extend our analysis to a more general framework. We estimate all deviations from exponential behavior at leading orders in the coupling constant.