Diffusion through a stochastic web

A connected web of stochasticity can be generated by a mapping derived from a linear oscillator perturbed by a periodic δ function. Such a stochastic web is useful for investigating global diffusion through a phase space in which the local diffusion within the web is nonuniform. An analytic expression for the global diffusion rate has been obtained using (1) the basic phase-space concept that the ergodic region is uniformly populated in the asymptotic limit, (2) a local calculation of the thickness of the stochastic web, and (3) the average local period for traversing a single mesh of the web. The results are compared with numerical computations of the diffusion rate and are found to be in good agreement. Although the linearity of the kicked oscillator leads to a connected grid in phase space, the diffusion rate, unlike Arnol’d diffusion, is related to that in two-dimensional phase space, with the diffusion coefficient D_{web≡Lrms²/T} scaling as K_α³, where K_α is a perturbation parameter. Discrepancies are discussed, and the effect of extrinsic stochasticity is briefly considered.