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# Review of 'Nonsmooth and level-resolved dynamics illustrated with the tight binding model'

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Thought provoking, a bit too formal, an experimental example would be welcome
 Average rating:     Rated 3.5 of 5. Level of importance:     Rated 3 of 5. Level of validity:     Rated 4 of 5. Level of completeness:     Rated 2 of 5. Level of comprehensibility:     Rated 4 of 5. Competing interests: None

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### Nonsmooth and level-resolved dynamics illustrated with the tight binding model

(2014)
We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function $$\sinc x \equiv \sin x / x$$. These physical effects appear in many systems with approximately equally spaced spectra, and is also robust for larger-amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven tight-binding model to illustrate these effects, both within and outside the perturbative regime.
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### Review information

10.14293/S2199-1006.1.SOR-PHYS.A2CEM4.v1.RYZTLS

This work has been published open access under Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com.

 ScienceOpen disciplines: Mathematical physics, Quantum physics & Field theory, Quantum gases & Cold atoms, Mathematical & Computational physics, Physics, Mathematics

### Review text

It would be nice if the authors could discuss more at length why their results do not invalidate the general use of Fermi's golden rule by physicists, and perhaps suggest a concrete experimental setup where this article would show all its relevance.