Fractional behavior in nonergodic reaction processes of isomerization

We present numerical evidence of fractional behavior in reactions for a prototype model of three-degree-of-freedom isomerization. The survival probability in the well exhibits two distinct ranges of time scales: one where it decreases with a power law, and the other where it decreases exponentially. Trajectories corresponding to power law decays exhibit 1/f spectra and subdiffusion in action space, and those with exponential decays exhibit Lorentzian spectra and normal diffusion. The existence of these two types of behavior is explained on the basis of nonergodicity in the network of nonlinear resonances (Arnold web) in the well, and connection between the saddle and the Arnold web. Implications of the fractional dynamics are discussed in terms of Maxwell's demon in molecules.