The transient properties of a Brownian particle moving in a bistable system with quantum corrections are investigated. The Quantum Smoluchowski Equation (QSE) is fully valid for high temperatures; for low temperatures it is valid only in a restricted domain of the state space. The quantum effects in a bistable system stand out for low temperatures. Explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The quantum effects are against the particle moving towards the destination from its original position.
 B. Q. Ai, X.J. Wang, G.T. Liu and L.G. Liu: “Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations”, Phys. Rev. E, Vol. 68, (2003), art. 061105; B.Q. Ai, X.J. Wang, G.T. Liu and L.G. Liu: “Correlated noise in a logistic growth model”, Phys. Rev. E, Vol. 67, (2003), art. 022903; B.Q. Ai, G.T. Liu, H.Z. Xie and L.G. Liu: “Efficiency and current in a correlated ratchet”, Chaos, Vol. 14, (2004), pp. 957–962.
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