Fluctuation spectra of weakly driven nonlinear systems

TL;DR

This paper investigates how weak periodic driving influences the fluctuation spectra of nonlinear systems, revealing additional spectral features like peaks or dips at specific frequencies, which depend sensitively on system parameters.

Contribution

It provides a unified analytical framework for understanding fluctuation spectra in various weakly driven nonlinear systems, including Brownian particles, two-state systems, and threshold detectors.

Findings

Spectral density shows peaks or dips at zero and driving frequencies.

Features are quadratic in the driving amplitude.

Analytical results match numerical simulations.

Abstract

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.