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We study the decay of a prepared state $E_0$ into a continuum {E_k} in thecase of non-Ohmic models. This means that the coupling is $|V_{k,0}| \propto|E_k-E_0|^{s-1}$ with $s \ne 1$. We find that irrespective of model detailsthere is a universal generalized Wigner time $t_0$ that characterizes theevolution of the survival probability $P_0(t)$. The generic decay behaviorwhich is implied by rate equation phenomenology is a slowing down stretchedexponential, reflecting the gradual resolution of the bandprofile. Butdepending on non-universal features of the model a power-law decay might takeover: it is only for an Ohmic coupling to the continuum that we get a robustexponential decay that is insensitive to the nature of the intra-continuumcouplings. The analysis highlights the co-existence of perturbative andnon-perturbative features in the dynamics. It turns out that there are specialcircumstances in which $t_0$ is reflected in the spreading process and not onlyin the survival probability, contrary to the naive linear response theoryexpectation.

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