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. (c) 2006 American Institute of Physics.