Stability, Isolated Chaos, and Superdiffusion in Nonequilibrium Many-Body Interacting Systems

We demonstrate that stability and chaotic-transport features of paradigmatic nonequilibrium many-body systems, i.e., periodically kicked and interacting particles, can deviate significantly from the expected ones of full instability and normal chaotic diffusion for arbitrarily strong chaos, arbitrary number of particles, and different interaction cases. We rigorously show that under the latter general conditions there exist {\em fully stable} orbits, accelerator-mode (AM) fixed points, performing ballistic motion in momentum. It is numerically shown that an {\em "isolated chaotic zone"} (ICZ), separated from the rest of the chaotic 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 and despite the fact that Kolmogorov-Arnol'd-Moser tori are not isolating. The time evolution of the mean kinetic energy of an initial ensemble containing an ICZ exhibits {\em superdiffusion} instead of normal chaotic diffusion.