Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight binding model

Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight binding model

Blog Article

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 read more 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 here outside the perturbative regime.