Stability, isolated chaos, and superdiffusion in nonequilibrium many-body interacting systems

We study stability and chaotic-transport features of paradigmatic nonequilibrium many-body systems, i.e., periodically kicked and interacting particles, for arbitrary number of particles, nonintegrability strength unbounded from above, and different interaction cases. We rigorously show that under the latter general conditions and in strong nonintegrability regimes there exist fully stable orbits, accelerator-mode (AM) fixed points, performing ballistic motion in momentum. These orbits exist despite of the completely and strongly chaotic phase space with generally fast Arnol'd diffusion. It is numerically shown that an "isolated chaotic zone" (ICZ), separated from the rest of the phase space, remains localized around an AM fixed point for long times even when this point is partially stable in only a few phase-space directions. This localization should reflect an Arnol'd diffusion in an ICZ much slower than that in the rest of phase space. The time evolution of the mean kinetic energy of an initial ensemble containing an ICZ exhibits superdiffusion instead of normal chaotic diffusion.