Multiplicative stochastic processes in nonlinear systems: Noise-induced transition from the overdamped to the inertial regime

Abstract

An experimental apparatus is set up to check, via analog circuits, the recent theoretical predictions of Graham and Schenzle [Phys. Rev. A 26, 1676 (1982)] on a Brownian particle with damping $\ensuremath{\gamma}$ in the presence of a fluctuating double-well potential, the fluctuations of which are characterized by the correlation time $\frac{1}{\ensuremath{\lambda}}$. They pointed out the basic role played in the overdamped regime by the parameter $r\ensuremath{\equiv}\frac{\ensuremath{\gamma}}{\ensuremath{\lambda}}$, which leads the system either to the It\^o regime ($r\ensuremath{\rightarrow}0$) or the Stratonovich one ($r\ensuremath{\rightarrow}\ensuremath{\infty}$). In the weak-noise region, these predictions are found to be correct. It is shown furthermore that with increasing intensity of the multiplicative noise the system exhibits a gradual transition from this to an inertial regime which can be accounted for by using the approach recently followed by Seshadri, West, and Lindenberg [Physica (Utrecht) A 107, 219 (1981)]. It is also shown that this transition is a synergic effect based on the cooperation of nonlinearity, inertia, and energy pumping.