Non-Stationary and Resonant Passage of a System: A High-Frequency Cutoff Noise

We study non-equilibrium behaviors of a particle subjected to high-frequency cutoff noise in terms generalized Langevin equation, where the spectrum internal is considered be Debye form. A closed solution impossible even if equation linear, because Laplace transform memory kernel multi-value function. use numerical method calculate velocity correlation function force-free and probability passing over top an inverse harmonic potential. indicate nonergodicity second type, i.e., auto-correlation approaches non-stationary at large times. Applied barrier passage problem, we find analyse resonant phenomenon that dependence frequency nonmonotonic when initial directional less than critical value, latter determined by equal 0.5.