Generic Superweak Chaos Induced by Hall Effect

Abstract

We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic ($\mathbf{B}$) and electric ($\mathbf{E}$) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of $B$ and $E$ and in the weak-chaos regime of sufficiently small nonintegrability parameter $κ$ (the kicking strength), there exists a \emph{generic} family of periodic kicking potentials for which the Hall effect from $\mathbf{B}$ and $\mathbf{E}$ significantly suppresses the weak chaos, replacing it by \emph{"superweak"} chaos (SWC). This means that the system behaves as if the kicking strength were $κ^2$ rather than $κ$. For $E=0$, SWC is known to be a classical fingerprint of quantum antiresonance but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small $κ$. In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.