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arXiv · 1912.04805

Generic shape of multichromatic resonance peaks

María Laura Olivera·Jesús Casado-Pascual·Sigmund Kohler
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Abstract

We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features. In particular, resonance peaks in the vicinity of commensurable frequencies possess a generic enveloping function whose width is inversely proportional to the averaging time. While the universal features can be derived analytically, the transition from the specific short-time behavior to the long-time limit is illustrated for the examples of a classical random walk and a dissipative two-level system both with biharmonic driving. In these models, the dependence of the time-averaged response on the relative phase between the two driving frequencies changes with increasing integration time. For short times, it exhibits the $2\pi$ periodicity of the dynamic equations, while in the long-time limit, the period becomes a fraction of this value.

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María Laura Olivera, Jesús Casado-Pascual, Sigmund Kohler. 2019-12-10. Generic shape of multichromatic resonance peaks. https://doi.org/10.1140/epjb%2Fe2020-100595-0

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