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Nonsmooth and level-resolved dynamics illustrated with a periodically  driven tight binding model

投到pra后被拒了。我打算利用这个机会全程记录和公开文章的审稿过程。下面是我们准备的回复。如有建议，望各位网友不吝赐教，在下不胜感激！

Dear Editor,

After careful consideration of the Referee report, we have decided to
resubmit the manuscript, together with a detailed justification
explaining what we think are the sources of misunderstanding.  

The point of the manuscript is not at all to re-derive Fermi's golden
rule, as the referee seems to have gathered.  We are somewhat
surprised by this interpretation, and we have revised the abstract and
introduction to properly hightlight the actual message of the
manuscript.  The main result is a discontinuous behavior (a sharp kink
or knee) as a function of time, periodically in time.  This effect can
indeed be derived from perturbation theory, which we have done, but
it's applicabilty goes well beyond a modified golden rule calculation,
as we have shown through results outside the perturbative regime.

We have revised our Abstract and Introduction significantly; we hope
the misunderstanding is now  avoided and the actual message of the
paper is clear.  

Below we give detailed responses to the referee comments.

Sincerely,

J.-M.Zhang and M.Haque

--------------------


 Referee: In this article, the authors "re-derive" first-order
 Fermi's Golden Rule with resonances.

Response: We find it very difficult to agree with this
interpretation/summmary of our work.

First, a summary of the manuscript that excludes any reference to the
physical effect treated here seems to us to be drastically
inappropriate.  The physical effect is a discontinuous behavior in
real-time dynamics as a function of time at long times, and an
associated level resolution visible only at long times.  

Second, the aim of the perturbative calculation (Section II) is not at
all to re-derive anything, but to demonstrate discontinuous features
(kinks) that appear periodically in the time evolution of physical
quantities, when the spectrum is roughly equally spaced.  To the best
of our knowledge, the appearance of this effect in perturbation theory
has not been shown or discussed in the literature.  Of course, we
could have missed such a treatment in our literature search --- if the
referee thinks this to be likely, it would be good to have a
reference.

(We are also not quite sure what Fermi's Golden `with resonances'
means.  Does that really have something to do with long-time
discontinuities in periodically driven systems?)

Third, the physical effect is not at all restricted to the
perturbative regime, and occurs also for strong driving.  We have
provided results from explicit calculations with TWO tight-binding
models (Section III), demonstrating this to be a generic effect not
dependent on any perturbative considerations.  Given these
non-perturbative calculations, it seems to us quite difficult to
justify the referee's highly incomplete summary of our work as a
re-derivation of a perturbative formalism.


 Referee: While they even comment very briefly on the fact, that
 there are cases where "the non-smoothness effect has been observed
 previously in the model of a single two-level atom interacting with
 a one-dimensional optical cavity," they take the smooth case (i.e.,
 no resonances) as the default and try to sell the case where the
 transition probability between two levels is not very smooth with a
 change of energy.

Response: The cited papers, where a non-smoothness effect was found,
do not recognize this to be a generic physical phenomenon and do not
find it from first-order perturbation theory, so the implication that
these previous papers provided the same or similar calculation is
incorrect.  We regret that our phrasing might have given this
impression.  We have now revised this paragraph thoroughly.

We find the second part of the Referee comment difficult to
understand, or to relate to the first part.  We have found a periodic
discontinuity in the time evolution, whose time scale (period) is
governed by the energy spacing.  Of course this does not appear in the
continuous case.  What are we "trying to sell" here?  (The unpleasant
phrasing even suggests that we are doing something dishonest.)  How
does the fact that we have identified a general phenomenon for
finite-size systems, contradict our pointing out that a specific
realization was previously observed in a specific model?

Finally, perhaps our presentation might have caused a series of
misunderstandings, but we find the description of our results to be
strikingly and disturbingly different from what they actually are: (1)
we are not looking at the transition ``between two levels'', but
rather at the transition from one level to an energy region with many
levels; (2) ``not very smooth with a change of energy'' is a very
peculiar description of the phenomenon presented: we have found kinks
as a function of time, not energy.


 Referee: I think this has been done in various forms thousands of
 times, and does not need a new paper.

Response: We thoroughly disagree.  However, we believe the
disagreement is because of a serious misreading of the actual results
presented in the paper.  This was perhaps caused by the way the
Abstract and Introduction was written in the first version.  We hope
that, with the rewritten Abstract and Introduction, the paper can be
judged for what it actually contains.

If it's really the case that the non-smooth strutures in time
evolution, as a generic phenomenon in driven systems, is actually
known in the literature, we would certainly like to see references.    


 Referee: In the case that I missed something really important, I am
 of course willing to take this into account. But in this case it has
 to be made really clear, already in abstract and introduction why
 this paper needs to be published. Some calculations involving
 Fourier transforms of functions involving the sinc function are
 definitely not sufficient.

Response: We agree that we have clearly failed to convey to the
referee the content of the paper, as seen by the wild divergence of
the Referee's description of the paper from the actual content.

Indeed, we should have focused more on making the results and their
contexts more clear in the Abstract and Introduction.  We believe that
the rewritten version remedies this issue.  Although the original
abstract and introdcution did mention the tight-binding systems quite
clearly, apparently they were not prominent enough for a casual
reading; we expect the new version to be even clearer in this regard,
so that the paper can no longer be mistaken to be merely "some
calculations involving the sinc function".