  Prevention of a quantum system's time evolution by repetitive, frequent
measurements of the system's state has been called the quantum Zeno effect (or
paradox). Here we investigate theoretically and numerically the effect of
repeated measurements on the quantum dynamics of the multilevel systems that
exhibit the quantum localization of the classical chaos. The analysis is based
on the wave function and Schroedinger equation, without introduction of the
density matrix. We show how the quantum Zeno effect in simple few-level systems
can be recovered and understood by formal modeling the measurement effect on
the dynamics by randomizing the phases of the measured states. Further the
similar analysis is extended to investigate of the dynamics of multilevel
systems driven by an intense external force and affected by frequent
measurement. We show that frequent measurements of such quantum systems results
in the delocalization of the quantum suppression of the classical chaos. This
result is the opposite of the quantum Zeno effect. The phenomenon of
delocalization of the quantum suppression and restoration of the classical-like
time evolution of these quasiclassical systems, owing to repetitive frequent
measurements, can therefore be called the 'quantum anti-Zeno effect'. From this
analysis we furthermore conclude that frequently or continuously observable
quasiclassical systems evolve basically in a classical manner.
