A new realistic Hamiltonian system is introduced, the "kicked Hall system''. This is a charged particle in a uniform magnetic field (in the z-direction) and in a uniform electric field (in the y-direction), periodically δ-kicked in time by a cosine potential with strength K in the x-direction. The electric-field strength is measured by a dimensionless parameter β. In the absence of an electric field (β=0) and under certain resonance conditions (i.e., precisely four kicks in one cyclotron period, as assumed in this work), it is well known that the system exhibits a global (unbounded) chaotic diffusion in the velocity plane for arbitrarily weak chaos (i.e., arbitrarily small K). This diffusion takes place on a stochastic web with square symmetry. The web structure and the diffusion rate strongly depend on the value of a conserved coordinate x_c of the cyclotron orbit center. In particular, for K << 1 and for very special values of x_c, the web thickness and the diffusion rate are much smaller than those for generic x_c. This phenomenon was first discovered as a classical fingerprint of quantum antiresonance in the β=0 system. We shall refer to this rare phenomenon for β=0 as "super-weak chaos''.

For β≠0, x_c is not conserved but varies linearly in time (Hall effect). We derive, for generic rational values of β/(2π), an exact expression of the effective integrable Hamiltonian H_eff  for the system up to (and including) second order in K; this Hamiltonian describes in an average sense the basic phase-space structure in the weak-chaos regime. We find that, except of essentially just two rational values of β/(2π), the first-order term of H_eff always vanishes while the second-order term is always independent of the initial value x_c⁽⁰⁾ of x_c, leading to a  stochastic web with a simple "universal" web skeleton. This precisely implies super-weak chaos on the universal web skeleton in a much more generic fashion that in the β=0 case.

For the two exceptional rational values of β/(2π), the leading-order term of H_eff is either linear or quadratic in K and depends on x_c⁽⁰⁾. We show that this term implies in both cases ballistic motion in velocity for generic x_c⁽⁰⁾, with a stochastic web arising only for special "critical" values x_cc⁽⁰⁾ of x_c⁽⁰⁾. The ballistic-transport rate vanishes like |x_c⁽⁰⁾ - x_cc⁽⁰⁾| as x_c⁽⁰⁾ approaches x_cc⁽⁰⁾.