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Classical "kicked Hall systems" (KHSs), i.e., periodically kicked charges inthe presence of uniform magnetic and electric fields that are perpendicular toeach other and to the kicking direction, have been introduced and studiedrecently. It was shown that KHSs exhibit, under generic conditions, thephenomenon of "superweak chaos" (SWC), i.e., for small kick strength $\kappa$ aKHS behaves as if this strength were effectively $\kappa^2$ rather than$\kappa$. Here we investigate quantum-dynamical and spectral manifestations ofthis generic SWC. We first derive general expressions for quantum effectiveHamiltonians for the KHSs. We then show that the phenomenon of quantumantiresonance (QAR), i.e., "frozen" quantum dynamics with flat quasienergy (QE)bands, takes place for integer values of a scaled Planck constant $\hbar_{\rms}$ and under the same generic conditions for SWC. This appears to be the mostgeneric occurrence of QAR in quantum systems. The vicinity of QAR is shown tocorrespond semiclassically to SWC. A global spectral manifestation of SWC isthe fact that a scaled QE spectrum as function of $\hbar_{\rm s}$, at fixedsmall value of $\kappa /\hbar_{\rm s}$, features an approximately "doubled"structure. In the case of standard (cosine) potentials, this structure is thatof a universal (parameters-independent) double Hofstadter butterfly. Also, forstandard potentials and for small $\hbar_{\rm s}$ (semiclassical regime), theevolution of the kinetic-energy expectation value exhibits a relatively slowquantum-diffusive behavior having universal features. These approximatespectral and quantum-dynamical universalities agree with predictions from theeffective Hamiltonian.

Kicked Hall Systems: Quantum-Dynamical and Spectral Manifestations of Generic Superweak Chaos