Shapiro steps in the steady-state dynamics of incommensurate structures

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Abstract
We consider the overdamped ac-driven dynamics of an incommensurate one-dimensional array of coupled oscillators in a spatially periodic substrate potential (Frenkel-Kontorova model) by means of molecular-dynamics simulations. The ac steady-state trajectories are described by a two-dimensional hull function which, as the strength of the substrate potential varies, undergoes a transition by the breaking of analyticity. This critical behavior is macroscopically observed as the appearance of Shapiro steps in the response function.