Linear response of a nonlinear stochastic oscillator

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Abstract
A nonlinear oscillator driven by both a coherent external field and a (weak) fluctuation-dissipation process of standard type is studied. It is shown that in the extremely-low-friction regime an additional random process comes into play which makes the linear-response theory work in spite of the scarce amount of standard fluctuation. This additional random process depends on the interplay of the nonlinear character of the oscillator under study and the weak fluctuation-dissipation process of standard type, but it is of transverse type, i.e., it does not involve any energy-dissipation process. On the theoretical side, this result rests on the joint use of a procedure of elimination of ‘‘irrelevant’’ variables and a rotating-wave-approximation technique which makes the role played by the transverse relaxation-process transparent. These predictions are checked by means of an analog experiment. Furthermore, light is shed onto an incorrect conclusion on the range of validity of the linear-response theory arrived at in an earlier report. This incorrect conclusion is now traced back to an ambiguous feature of the experimental results. The frequency position of the absorption peak does not change significantly upon increase of the excitation field up to a certain value of the excitation field. After this initial plateau the frequency of the absorption peak exhibits a rapid increase with increasing the intensity of the radiation field. Then the increase of the linewidth of the absorption peak becomes slower again with a parallel slow increase of the linewidth of the absorption spectrum, the shape of which, furthermore, does not show any sign of saturation, thereby generating the false impression, when the experimental investigation is carried out in this region, of a complete breakdown of the linear-response theory.