  We investigate classical-quantum correspondence for kicked Harper model for
extremely small values of the Planck constant $\hbar$. In the asymmetric case a
pure quantum state shows clear signature of classical diffusive as well as
super diffusive transitions asymptotically independent of $\hbar$. However, for
the symmetric case, the $\hbar$ independent behavior occurs only for
renormalized parameter $\bar{K}=K/(2\hbar)$ with intriguing features such as a
sharp transition from integrable to non-integrable transport at
$\bar{K}=\pi/2$, a series of transitions at multiples of $\pi$ and periodicity
of the transmission probability. These results add new puzzles to the frontiers
of quantum chaos.
