  Coherent dynamics of atomic matter waves in a standing-wave laser field is
studied. In the dressed-state picture, wave packets of ballistic two-level
atoms propagate simultaneously in two optical potentials. The probability to
make a transition from one potential to another one is maximal when centroids
of wave packets cross the field nodes and is given by a simple formula with the
single exponent, the Landau--Zener parameter $\kappa$. If $\kappa \gg 1$, the
motion is essentially adiabatic. If $\kappa \ll 1$, it is (almost) resonant and
periodic. If $\kappa \simeq 1$, atom makes nonadiabatic transitions with a
splitting of its wave packet at each node and strong complexification of the
wave function as compared to the two other cases. This effect is referred as
nonadiabatic quantum chaos. Proliferation of wave packets at $\kappa \simeq 1$
is shown to be connected closely with chaotic center-of-mass motion in the
semiclassical theory of point-like atoms with positive values of the maximal
Lyapunov exponent. The quantum-classical correspondence established is
justified by the fact that the Landau--Zener parameter $\kappa$ specifies the
regime of the semiclassical dynamical chaos in the map simulating chaotic
center-of-mass motion. Manifestations of nonadiabatic quantum chaos are found
in the behavior of the momentum and position probabilities.
