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The time-dependent barrier passage of an anomalous system-reservoir couplingnon-equilibrium open environment is studied where the heat bath is modulated byan external noise. The time-dependent barrier passing probability is obtainedanalytically by solving the generalized Langevin equation. The escaping rateand effective transmission coefficient are calculated by using of the reactiveflux method in the particular case of external $\delta$-correlated noisemodulated internal Ornstein-Uhlenbeck process. It is found that not all thecases of external noise modulating is harmful to the rate process. Sometimes itis even beneficial to the diffusion of the particle. There exists an optimalstrength of external noise modulation for the particle to obtain a biggestprobability to escape from the potential well to form a notable rate ofeffective net flux.

Time-dependent barrier passage in External Noise Modulated System-reservoir Environment