之前投到JPA的文章刚刚收到审稿意见。两个都同意，接收。

感觉审稿人没花心思看文章，估计如一个朋友所做的，把文章放1个月，然后想起来要交审稿意见了，借着蹲马桶的功夫看了遍，回来就写了意见。

JPhysA-112154.pdf

之前这个文章投pra不送审（估计傻逼编辑看到是在讨论无限深方势阱。其实我们才真正理解了之前很多pra文章报道的非平方衰变现象背后的机理，还指出了新的可能）。投epl后，收到两个意见，其中一个被编辑删除，拒稿。学生很受打击。

这是当初一个小想法导致的第5篇文章。搞不好还可以再写。

Dear Dr Zhang,

Re: "Inferring  the smoothness of  the autocorrelation function from that of the initial state" by Yang, K.L; Zhang, Jiang min

Article reference: JPhysA-112154

We are pleased to tell you that we have provisionally accepted your Paper for publication in Journal of Physics A: Mathematical and Theoretical. Any further comments from the referees can be found below and/or attached to this message. Our editorial team will now perform some final checks to ensure that we have everything we need to publish your Paper. These checks will enable our production team to publish your Paper as quickly and efficiently as possible. Once this is confirmed, your article will be formally accepted and we will inform you of this via email.

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REFEREE REPORT(S):

Referee: 1

COMMENTS TO THE AUTHOR(S)

Authors consider three kind of initial states into the infinite well potential and studied its evolution showing that the decay power law at very short times depends of the of the smoothness of the initial state. They use the well-known survival probability to show it. The novelty of this study is the fact extends to other power law $t^\beta$The novelty of this study is the fact extends to other power law $t^\beta$ (at this point, authors may or not include an analysis of of the statistical properties of initial states, because this suggest that the decay power law depends on it).

The paper is well written, it is self-content providing an easy lecture. Thus I recommend to publication in J. Phys. A 

Referee: 2

COMMENTS TO THE AUTHOR(S)

Report on the manuscript No JPhysA-112154

"Inferring the smoothness of the autocorrelation function from that of the initial state"

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The autocorrelation function (or survival probability), $A(t)$, is studied in the paper considered. This quantity is extremely important in quantum optics and in quantum theory of unstable states. Authors make use of the Fourier analysis  in their research and find connections between the  smoothness of the autocorrelation function and the speed of the decay process: They show that the more smooth functions the faster decay and vice versa. They use a simple solvable model, where  the particle  can move only   inside the well  bounded by walls at points  $0$ and $\pi$, (The well is on the interval   $(0,\pi)$).  Nevertheless, their results are general and valid in much more complicated systems.

They analyze a three chosen initial states denoted as $\psi_{1}, \psi_{2}, \psi_{3}$ and find Fourier series representation of these states which allows them to find finally corresponding autocorrelation functions $A_{1}(t), A_{2}(t), A_{3}(t)$. Next, the authors focus their attention on finding properties of these autocorrelation functions at  short times area, for $t \to 0$. It was done using Mellin transforms method. They found that some survival amplitudes behave nonquadrtically at short times and that this fractional power law behavior depend on the smoothness of the initial state. They show that the smoothness or nonsmoothness of an initial state affects not only the differentability of the autocorrelation function as a whole but also its short-time behavior. These results are especially important for them who study quantum Zeno effect and try to observe it, and for physicists  conducting research in the field of quantum optics and solid state physics.

Summing up: I recommend to publish this paper.