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

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:

Reviewed article

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  • Abstract: found
  • Article: found
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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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    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.


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