Generic shape of multichromatic resonance peaks
arXiv:1912.04805 · doi:10.1140/epjb/e2020-100595-0
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 periodicity of the dynamic equations, while in the long-time limit, the period becomes a fraction of this value.
arXiv comment8 pages, 6 figures
References in corpus (16)
- Brownian motors: noisy transport far from equilibrium
- Artificial Brownian motors: Controlling transport on the nanoscale
- Driven quantum transport on the nanoscale
- Directed current due to broken time-space symmetry
- Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
- Frequency and Phase Synchronization in Stochastic Systems
- Quantum Stochastic Synchronization
- Rectification of laser-induced electronic transport through molecules
- Two-state theory of nonlinear Stochastic Resonance
- Theory of frequency and phase synchronization in a rocked bistable stochastic system
- Landau-Zener interference at bichromatic driving
- General approach for dealing with dynamical systems with spatiotemporal periodicities
- Asymptotic theory of quasiperiodically driven quantum systems
- Lissajous rocking ratchet
- Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing
- Avoided crossing and sub-Fourier sensitivity in driven quantum systems