Scaling and critical-like behavior in multidimensional diffusive dynamics

The intermediate time dependence of the survival probability in two-dimensional diffusive dynamics is investigated on a model myoglobin-CO potential-energy surface. For small diffusion anisotropy, we derive a scaling relation for the characteristic time and exponent of the observed power-law dependence, which is verified by exact two-dimensional calculations. At higher anisotropy values, we report a critical-like jump in the anisotropy dependence of the power-law exponent. Possible experimental implications are discussed.