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

Abstract

We study the decay of a prepared state E(0) into a continuum {E(k)} in the case of non-Ohmic models. This means that the coupling is |V(k),(0)| proportional to |E(k)-E(0)|(s-1) with s not equal 1. We find that irrespective of model details there is a universal generalized Wigner time t(0) that characterizes the decay of the survival probability P(0)(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 t(0) is reflected in the spreading process and not only in the survival probability, contrary to the naive linear-response theory expectation.