博文
一千个审稿人有一千个不同的意见
||
之前被AJP拒的文章转投EJP了。刚刚收到2个审稿意见。
这次都是正面的。而且意见跟之前AJP的三个审稿人的意见没有任何重复之处。这再次证明，一千个读者心目中有一千个哈姆雷特，一千个审稿人有一千个不同的意见。
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
Body:
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.
Yours sincerely
Kit Durant
On behalf of the IOP peer-review team:
Dr Ben Sheard - Editor
Kit Durant – Associate Editor
Lucy Joy – Editorial Assistant
ejp@iop.org
and Iain Trotter – Associate Publisher
IOP Publishing
Temple Circus, Temple Way, Bristol
BS1 6HG, UK
www.iopscience.org/ejp
===================================================================
REFEREE REPORT(S):
Referee: 1
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.
===================================================================
Referee: 2
COMMENTS TO THE AUTHOR(S)
See attached.
This paper is devoted to the derivation of Fermi’s golden rule for a model, which
author has termed as “ideal model” with quasi-continuum of equidistant energy levelsby using Poisson summation formula. The ideal model is also employed to demonstrate decaying evolution by using Dyson perturbation series and Poisson summation formula. The manuscript reports new results and it can be published in Eur. J. Physics. In order to enhance the readability author may take following suggestion into account:(1) Since the paper is for pedagogic purpose it would be beneficial to readers if a brief derivation of the Hamiltonian is provided.(2) This model appears to be equivalent to single cavity mode interacting with twolevelatom. For multimode there should be another summation index over various modes as considered in Weisskopf-Wigner approach.(3) In the derivation of exponential decay author should explicitly mention the role of continuum approximation. It is important to bring out under what condition the coherent dynamics changes to an incoherent one.
修改后，referee 2还有点小问题：
I have gone through the response of the authors on the comments of reviewers. With respect to the response provided by the authors on my 3rd question I wish to clarify that by coherent I mean oscillatory solution and incoherent denotes exponentially decaying solution. In case of oscillatory solution that norm of the wave function remains conserved, which is characteristic of hermitian Hamiltonian, on the other hand, for decaying solution norm does not remain conserved. In case of coherent process energy is exchanged periodically between the two systems. On the other hand, in incoherent energy leaks out from smaller system to larger system (with continuum energy spectrum). In Weisskopf-Wigner or Master equation approach a condition on the bandwidth of the large system (reservoir/continuum) is invoked to get dissipation. I request authors to clarify this issue and then manuscript may be accepted for publication in EJP.
我们的回复：
Thank you very much for your clarification. We now understand the problem. Yes, indeed, the continuum is essential for the exponential decay. To have an incoherent dynamics of the discrete level |brangle, we need sufficiently many partner levels in the continuum. Moreover, now we see that we also need the level spacing to be small enough, otherwise the Heisenberg time is too short and the revivals are relevant.
We have thus added a paragraph at the end of Section 4.
We hope now it is okay.
===========================
List of changes:
(1) The last paragraph of Sec. 4 is new.
(2) Ref. 34 is new.
之后文章被接收。历时70天。
Fermi golden rule its derivation and breakdown by an ideal model.pdf
投稿与审稿
https://blog.sciencenet.cn/blog-100379-996143.html
上一篇：美国物理杂志（AJP）的标准有多高？
下一篇：国基意见（差得一塌糊涂）
