Fluctuation and dissipation of a stochastic micro-oscillator under delayed feedback

We investigate the dynamics of a microcantilever subjected to the combined forcing from Brownian motion and delayed self-feedback. Specifically, the excitation of the fundamental mode of the cantilever by thermomechanical agitation is utilized as delayed external forcing and the resulting dynamical response is studied as a function of the delay and the coupling strength. A fluctuation-dissipation theorem is derived from the delay Langevin-like equation and its validity is discussed. The relaxation time scale associated with the adsorption processes is established and an experiment to determine the oscillator's effective temperature is proposed.