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

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      Abstract

      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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        Quantum-optical analogies using photonic structures

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            Author and article information

            Journal
            16 April 2014
            2015-09-23
            1404.4280 10.14293/S2199-1006.1.SOR-PHYS.A2CEM4.v1

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            Link with the Paley-Wiener theorem and another reference is added; any comment is welcome and will be greatly appreciated!
            cond-mat.quant-gas math-ph math.MP quant-ph

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