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The time-dependent barrier passage of an anomalous damping system is studiedvia the generalized Langevin equation (GLE) with non-Ohmic memory dampingfriction tensor and corresponding thermal colored noise tensor describing aparticle passing over the saddle point of a two-dimensional quadratic potentialenergy surface. The time-dependent passing probability and transmissioncoefficient are analytically obtained by using of the reactive flux method. Thelong memory aspect of friction is revealed to originate a non-monotonic$\delta$(power exponent of the friction) dependence of the passing probability,the optimal incident angle of the particle and the steady anomaloustransmission coefficient. In the long time limit a bigger steady transmissioncoefficient is obtained which means less barrier recrossing than theone-dimensional case.

Time-dependent barrier passage of Two-dimensional non-Ohmic damping system