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

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 τ is revealed: all of the quantities measured are a function of ${\tau }^2$. In particular, the escape rate in a quartic double-well potential decreases exponentially with increasing ${\tau }^2$. The relevant spatial spectral densities are also determined for both the monostable and the bistable quartic potential on varying τ. Previous theoretical predictions for the white-noise (τ=0) limit are thus checked. The frequency of the resonance peak is shown to shift depending on ${\tau }^2$. Finally, some effort has been paid at justifying theoretically the results obtained.