Generic shape of multichromatic resonance peaks

María Laura Olivera-Atencio (), Jesús Casado-Pascual () and Sigmund Kohler ()
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María Laura Olivera-Atencio: Física Teórica, Universidad de Sevilla
Jesús Casado-Pascual: Física Teórica, Universidad de Sevilla
Sigmund Kohler: Instituto de Ciencia de Materiales de Madrid, CSIC

The European Physical Journal B: Condensed Matter and Complex Systems, 2020, vol. 93, issue 2, 1-9

Abstract: 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 2π periodicity of the dynamic equations, while in the long-time limit, the period becomes a fraction of this value. Graphical abstract

Date: 2020
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DOI: 10.1140/epjb/e2020-100595-0

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