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

    Nonsmooth and level-resolved dynamics illustrated with the tight binding modelCrossref
    Paper needs further improvements and clarifications
    Average rating:
        Rated 2 of 5.
    Level of importance:
        Rated 2 of 5.
    Level of validity:
        Rated 2 of 5.
    Level of completeness:
        Rated 2 of 5.
    Level of comprehensibility:
        Rated 2 of 5.
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    Nonsmooth and level-resolved dynamics illustrated with the tight binding model

    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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      I suggest revising the paper by reducing the emphasis on the kinks and focus more on tight binding model and also the features of the analytic form of Eq. 10. After that the paper might be suitable for publication.


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