Stochastic resonant behaviours and steady state control in harmonic systems

Adrian Rubio Universidad de Santiago de Chile

Brownian motion and parametric resonance are two paradigmatic phenomena particularly taking place on harmonic dynamical systems, covering a plethora of branches in science. While the former gives a pathway to include dissipation and noise (additive noise) in a system, the latter stands for a physical mechanism that supplies energy to a system by exploiting the resonant variation of the characteristic frequency. Both aspects find their syncretism in the so-called stochastic resonance, where the competition between dissipation and the strength of the fluctuations in the characteristic frequency of the system (multiplicative noise) defines whether the system undergoes exponential growth (as in parametric resonance) or stabilises in a steady state in the long-time limit[1]. Typically, the impact of this competition is neglected due to relatively high dissipation rates that overcome resonant effects. However, the development of harmonic systems with increasingly quality factors makes this competition to come into play, raising as a potential limiting factor but also as a possibility for a novel control mechanism. In this talk, I will introduce the basics of the mentioned dynamical phenomena to quantify its impact on experimental setups, such as optically levitated nanoparticle. Moreover, I will also show how these concepts enter interacting harmonic systems, giving place to enhanced resonant behaviours in the steady state. The latter can be exploited, for instance, for heat transport and thermalisation[2].

[1] B. J. West, K. Lindenberg and V. Seshadri, Physica 102A, pp. 470-488 (1980).

[2] A. E. Rubio Lopez and F. Herrera, Stochastic resonant behaviours and steady state control in harmonic systems, in preparation.