Harmonic Noise-Induced Resonant Passing in an Inverse Harmonic Potential

The problem of a Brownian particle driven by harmonic noise passing over the saddle point in an inverse harmonic potential is studied. The passing probability over the saddle point is obtained analytically. The stationary passing probability is found to arrive at its maximal value when the frequency parameter of the harmonic noise is close to the frequency of the inverse harmonic potential, which results in a resonance phenomenon. With an increase in the frequency parameter of noise, the Brownian particle will recross the barrier, thereby increasing the escape rate and resulting in a decrease in the passing probability.