Fractional behavior in multidimensional Hamiltonian systems describing reactions

The fractional behavior is presented for a minimal Hamiltonian system of three degrees of freedom which describes reaction processes. The model has a double-well potential where the Arnold web within the well is nonuniform. The survival probability within the well exhibits power law decay in addition to exponential decay. Moreover, the trajectories of the power law decay exhibit 1/f spectra and subdiffusion in the action space, while the trajectories of the exponential decay show Lorentzian spectra and normal diffusion. Transient features of these statistical properties reveal the dynamical connection, i.e., how trajectories approach to (depart from) the Arnold web from (to) the region around the potential saddle. In particular, a wavelet analysis enables us to extract transient features of the resonances. Based on these results, we suggest that resonance junctions including higher-order resonances are important for understanding the dynamical origins of the fractional behavior in reaction processes.