We present evidence that anomalous transport in the classical standard map
results in strong enhancement of fluctuations in the localization length of
quasienergy states in the corresponding quantum dynamics. This generic eff
ect occurs even far from the semiclassical limit and reflects the interplay
of local and global quantum suppression mechanisms of classically chaotic
dynamics. Possible experimental scenarios an also discussed. [S1063-651X(99
)03006-8].