Fluctuation spectra of weakly driven nonlinear systems

We show that in periodically driven systems, along with the delta-peak at the driving frequency, the spectral density of fluctuations displays extra features. These can be peaks or dips with height quadratic in the driving amplitude, for weak driving. For systems where inertial effects can be disregarded, the peaks/dips are generally located at zero frequency and at the driving frequency. The shape and intensity of the spectra very sensitively depend on the parameters of the system dynamics. To illustrate this sensitivity and the generality of the effect, we study three types of systems: an overdamped Brownian particle (e.g., an optically trapped particle), a two-state system that switches between the states at random, and a noisy threshold detector. The analytical results are in excellent agreement with numerical simulations.