  The quantum kicked particle in a magnetic field is studied in a weak-chaos
regime under realistic conditions, i.e., for {\em general} values of the
conserved coordinate $x_{{\rm c}}$ of the cyclotron orbit center. The system
exhibits spectral structures [``Hofstadter butterflies'' (HBs)] and quantum
diffusion depending sensitively on $x_{{\rm c}}$. Most significant changes take
place when $x_{{\rm c}}$ approaches the value at which quantum antiresonance
(exactly periodic recurrences) can occur: the HB essentially ``doubles'' and
the quantum-diffusion coefficient $D(x_{{\rm c}})$ is strongly reduced. An
explanation of these phenomena, including an approximate formula for $D(x_{{\rm
c}})$ in a class of wave packets, is given on the basis of an effective
Hamiltonian which is derived as a power expansion in a small parameter. The
global quantum diffusion of a two-dimensional wave packet for all $x_{{\rm c}}$
is briefly considered.
