Osciladores parametricamente forçados na presença de ruído térmico.

Abstract

Here we report a theoretical model based on Green’s functions and on techniques of the theory of averaging that describes the dynamics of parametrically-driven oscillators under the action of additive thermal noise. Our stochastic dynamics model gives quantitative estimates for heating and quadrature thermal noise squeezing near the first parametric instability zone of the oscillator. Specifically, we obtain a perturbative approximation of the oscillator’s Green’s function and, subsequently, give estimates to the statistical fluctuations hx2(t)i, where x(t) is the position of the oscillator, and hv2(t)i, where v(t) represents the velocity of the oscillator. Furthermore, we investigate the phenomenon of parametric amplification and propose analytical estimates of the signal-to-noise ratio. The results imply that parametric amplifiers can be excellent detectors, because they can have extremely high values of the signal to noise ratio as well as a narrow bandwidth. We also observe that this model can be applied to investigate the dynamics of several other physical systems such as ion guides, ion traps, and axially loaded microelectromechanical devices.