Multi-extreme behavior and giant suppression plateau of activation rate in a periodic system driven by correlated noise

An analytical investigation of the activation rate for Brownian particle in a periodic system driven by cross-correlated Gaussian white noises is presented. As used in the literature the activation rate kappa is defined as the inverse of the mean first-passage time and the relative activation rate nu = kappa/kappa (S) in which kappa (S) indicates the rate in the Smoluchowski limit, the Limit of the multiplicative to additive noise strength ratio R = 0. The center idea of this Letter is to construct an exact soluble model in order to exhibit the possible new effect of the cross-correlated Gaussian white noises on the activation processes. The model clearly shows the following novel activation phenomena. (1) There is one and only extreme (minimum) in the nu similar to R curve for the case of positive correlation. However, for independent noises case the nu similar to R curve is monotonously varied. In other words, the positive correlation leads to the suppression of the activation rate. (2) When the two noises are negative correlative, the nu similar to R curves exist as three types of shape, that is, the non-extreme, the two-extreme, and the four-extreme shape. (3) In the intense negative correlation region, the nu similar to R curve experiences a re-entrant transition between the different types of shape. (4) The nu similar to R curve exhibits a giant suppression plateau when the two noises are intense positive correlation. The mechanism for the appearance of this giant suppression plateau is discussed. (C) 2001 Elsevier Science B.V. All rights reserved.