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REFEREE A

The authors suggest a particular procedure involving coarse-graining of non-smooth energy spectra of certain driven systems and use it to draw conclusions regarding long-time deviations from the Golden Rule.
I find the paper unsuitable for publication for the following reasons:
1. The authors ignore the extensive literature concerning anomalous decay of driven and non driven systems to a continuum or a bath. This literature addresses essentially the same problem as the present paper, i.e. the breakdown of Fermi's Golden Rule. Without a detailed comparison with this literature, it is unclear whether there is novelty or merit in the present model. Here is a partial list of the relevant literature:
A.G.Kofman and G.Kurizki,PRA 54, R3750 (1996); Nature 405, 546(2000);
PRL 87, 270405 (2001);IEEE trans. nanotechnology 4, 116 (2005);A.Barone et al. PRL 92, 200403 (2004) are all about the breakdown of the Golden Rule under driving or free evolution at short times, but the principles are similar  to those of a long-time treatment .
A.G. Kofman et al. J.Mod.Opt. 41, 353 (1994) is a general treatment of such breakdown, with explicit analysis of the long-time limit, in which the
present model is supposed to apply.
I.E.Mazets et al. PRL 94, 190403 (2005) and N.Bar Gill et al. PRL 102, 110401 (2009) are theoretical and experimental studies, respectively, of such effects at short times in a tight-binding model.
Finally,G.Gordon et al. NJP 12, 053033 (2010) have extended this notion to multilevel systems and long times.
2. The authors use the terms stimulated absorption and radiation improperly. They should consult textbooks on QED or Quantum Optics to see what is wrong.
3. Most importantly, the mathematical assumptions underlying Eq. (3) are
too restrictive to claim physical relevance or interest of the model. Why should such a contrived model and its tedious analysis be of interest? What does it teach us about physical behaviour? Not much, I am afraid.
To conclude, without a discussion of what is principally  new compared to the literature above, and without a convincing physical motivation and arguments regarding the significance of the results, the paper cannot qualify for publication.

REFEREE B

The authors consider possible nonsmooth behaviour of transition probability
in time, in particular possible kinks in its time dependence occuring for
systems with almost equally spaced levels. The result is traced back to a
simple equality concerning sinc function.
While the results is, I believe new, and to some extend amusing (showing
the authors' expertise  in handling summation formulae) I fail to see
sufficient importance to warrant publication in EPL which
... publishes original, high-quality letters in all areas of physics, from
condensed matter and interdisciplinary research to astrophysics and plasma
science. Articles must contain sufficient argument and supporting
information to satisfy workers in the field, and be of interest and
importance to one or several sections of the physics community.

The result is based on two assumptions - almost equal spacing of levels
and similar coupling  amplitudes for all of them. Then, as shown on
exemplary system, even the exact simulation shows piecewise linear survival
probability. I find nothing wrong with that result, Have not been aware of
it, still it seems to be a little more than the curiosity.