  The time-dependent barrier passage of an anomalous damping system is studied
via the generalized Langevin equation (GLE) with non-Ohmic memory damping
friction tensor and corresponding thermal colored noise tensor describing a
particle passing over the saddle point of a two-dimensional quadratic potential
energy surface. The time-dependent passing probability and transmission
coefficient are analytically obtained by using of the reactive flux method. The
long 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 anomalous
transmission coefficient. In the long time limit a bigger steady transmission
coefficient is obtained which means less barrier recrossing than the
one-dimensional case.
