Generic shape of multichromatic resonance peaks

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2020-02, Vol.93 (2), Article 30
• Main Authors: Olivera-Atencio, María Laura, Casado-Pascual, Jesús, Kohler, Sigmund
• Format: Article
• Language: English
• Subjects: Advances in Quasi-Periodic and Non-Commensurate Systems; Complex Systems; Condensed Matter Physics; Fluid- and Aerodynamics; Periodic variations; Physics; Physics and Astronomy; Random walk; Regular Article; Resonance; Solid State Physics; Time dependence
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2020-100595-0

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