Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum

We study the decay of a prepared state E0 into a continuum {Ek} in the case of non-Ohmic models. This means that the coupling is | Vk,0|^|Ek ^- E0 ^| s^-1 with s 1. We find that irrespective of model details there is a universal generalized Wigner time t0 that characterizes the decay of the survival probability P0 (t). The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the band profile. But depending on nonuniversal features of the model a power-law decay might take over: it is only for an Ohmic coupling to the continuum that we get a robust exponential decay that is insensitive to the nature of the intracontinuum couplings. The analysis highlights the coexistence of perturbative and nonperturbative features in the dynamics. It turns out that there are special circumstances in which t0 is reflected in the spreading process and not only in the survival probability, contrary to the naive linear-response theory expectation.