这次是一个伊朗博士后。
Although the paper seem to be a bit confusing, as a condensed matter physicist, I do find the results interesting. I have noticed that the kinks seen in the paper is an old topics in the field of AMO which goes back to as early as 1986 (e.g. Phys. Rev. A. 35, 4226 (1987) by J. Parker. ). Nonetheless, I have following comments and questions,
1. The central result of the paper seems to be rewriting Eq. 5 in the form of Eq. 10. I suggest to emphasize more on the advantage of the new formula. Furthermore, I can see that Eq 10 can be summed over to obtain an analytic expression.
2. In Fig. 1c it would have been better to include alpha=0.4 and, if possible, explain why there is an overlap with alpha=0.2.
3. If I understand correctly, the motivation for considering tight binding Hamiltonian is to have varying energy level spacing. I would suggest the author clarify how the DoS can alter the periodicity of the kinks.

有趣的是，他发现了一个1986年的文章，里面也出现了kink。不过，作者没有发现背后的数学。

很纳闷他是怎么发现的。一个搞凝聚态的怎么发现一个AMO领域的文章？检索什么关键词？

他的第二点是错的。如果是在传统的审稿系统里，我们得小心翼翼地给他指出，不能得罪他。在目前的系统下，一切公开透明，参与到这里来的人都是open minded的，直接指出就行了。

开放评审很有意思！

ps: 转眼收到第三个。这次是个南非开普顿大学做宇宙学的博士生

I found this paper an interesting work on perturbation theory. I think, for a better readership, the paper could benefit from
1. a brief discussion on the regime of linearity of perturbations and when this linearity breaks down and
2. a quantitative clarification of such propositions as assumptions being "only approximately satisfied", the level spacing and coupling strength being "slowly varying", etc...

As indicated by the authors' own admission, the results of the paper are relevant only to single particle models in one dimension. It might be worthwhile mentioning if there are any attempts/prospects to generalize this work.

I also wonder if using the normalized sinc function, rather than the sinc function, would be any more convenient.

对比目前收到的三个意见和之前在pra和epl收到的三个意见，目前的三个意见积极正面得多。这三个意见都用了interesting这个词，但是之前的三个只有一个用这个词。