第一个审稿人显然是数学物理专家，发过communications of mathematical physics（我心目中的顶级期刊，秒杀prl）多篇。
Subject: Our initial decision on your article: EJP-102152
Dear Dr Zhang,
Re: "Fermi's golden rule: its derivation and breakdown by an ideal model" by Zhang, Jiang min
Article reference: EJP-102152
We have now received the referee report(s) on your Paper, which is being considered by European Journal of Physics.
The referee(s) have recommended that you make some amendments to your article. The referee report(s) can be found below and/or attached to this message. You can also access the reports at your Author Centre, at https://mc04.manuscriptcentral.com/ejp-eps
Please consider the referee comments and amend your article according to the recommendations. You should then send us the final version together with point-by-point replies to the referee comments and a list of the changes you have made. Please upload the final version and electronic source files to your Author Centre by 26-Aug-2016.
If we do not receive your article by this date, it may be treated as a new submission, so please let us know if you will need more time.
We look forward to hearing from you soon.
On behalf of the IOP peer-review team:
Dr Ben Sheard - Editor
Kit Durant – Associate Editor
Lucy Joy – Editorial Assistant
and Iain Trotter – Associate Publisher
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COMMENTS TO THE AUTHOR(S)
This is a very well written paper which deals with fundamental issues such as the survival probability and Fermi's Golden Rule. The author chose to work with a rather simple model in which the survival probability can be expressed quite explicitly and studied as a function of different parameters which characterize the model.
The results are quite transparent and useful since they can be easily understood without a deeper knowledge of functional analysis. I therefore recommend publication, provided the comments below are addressed and commented briefly in the manuscript.
I. During the last 20 years, the mathematical community has achieved a deep understanding of
the survival probability via resonant states, and/or uniform time evolution. The list of references is huge.
Here are a few very important ones:
1. Cattaneo L., Graf G.M., Hunziker W.: A general resonance theory based on Mourre’s inequality. Ann. H. Poincaré 7, 583–614 (2006)
2. Dinu V., Jensen A., Nenciu G.: Perturbation of near threshold eigenvalues: crossover from exponential to non-exponential decay laws. Rev. Math. Phys. 23, 83–125 (2011)
3. Jensen A., Nenciu G.: The Fermi golden rule and its form at thresholds in odd dimensions. Commun. Math. Phys. 261, 693–727 (2006)
The main inconvenient with these works is that the mathematical level is typically way above the understanding of an average physicist.
II. Note that in the simple model used in the manuscript it is crucial to have the coupling constant g different from zero, otherwise no resonant effects can occur. However, one can try to draw a parallel between section 4 of this manuscript and the much more general results of the following paper which can also deal with a vanishing g:
Cornean H.D., Jensen A., Nenciu G.: Metastable States When the Fermi Golden Rule Constant Vanishes, Commun. Math. Phys. 334(3), 1189–1218 (2015).
More precisely, look at formulas (1.2) and (1.3) and the problem formulation in the above paper. One can see that the exponential decay of the survival probability is again only valid for limited times determined by the imaginary part of the resonance, while for large times the decay typically becomes only polynomial. In other words, for very large times, the pure exponential decay is not true, for a very large class of relevant physical system.
COMMENTS TO THE AUTHOR(S)
This paper is devoted to the derivation of Fermi’s golden rule for a model, whichauthor has termed as “ideal model” with quasi-continuum of equidistant energy levelsby using Poisson summation formula. The ideal model is also employed todemonstrate decaying evolution by using Dyson perturbation series and Poissonsummation formula. The manuscript reports new results and it can be published inEur. J. Physics. In order to enhance the readability author may take followingsuggestion into account1) Since the paper is for pedagogic purpose it would be beneficial to readers if abrief derivation of the Hamiltonian is provided.(2) This model appears to be equivalent to single cavity mode interacting with twolevelatom. For multi-mode there should be another summation index over variousmodes as considered in Weisskopf-Wigner approach.(3) In the derivation of exponential decay author should explicitly mention the role ofcontinuum approximation. It is important to bring out under what condition thecoherent dynamics changes to an incoherent one.