Analog simulation of underdamped stochastic systems driven by colored noise: Spectral densities

Abstract

Stochastic relaxation in underdamped nonlinear potentials driven by exponentially time-correlated noise is studied thoroughly by means of analog simulation. The experimental data reported herein should help to tie down future theoretical investigations. A novel dependence of the observed quantities on the noise correlation time \ensuremath{\tau} is revealed: all of the quantities measured are a function of ${\ensuremath{\tau}}^{2}$. In particular, the escape rate in a quartic double-well potential decreases exponentially with increasing ${\ensuremath{\tau}}^{2}$. The relevant spatial spectral densities are also determined for both the monostable and the bistable quartic potential on varying \ensuremath{\tau}. Previous theoretical predictions for the white-noise (\ensuremath{\tau}=0) limit are thus checked. The frequency of the resonance peak is shown to shift depending on ${\ensuremath{\tau}}^{2}$. Finally, some effort has been paid at justifying theoretically the results obtained.