  The enhancement of tunneling probability in the nearly integrable system is
closely examined, focusing on tunneling splittings plotted as a function of the
inverse of the Planck's constant. On the basis of the analysis using the
absorber which efficiently suppresses the coupling creating spikes in the plot,
we found that the splitting curve should be viewed as the staircase-shaped
skeleton accompanied by spikes. We further introduce renormalized integrable
Hamiltonians, and explore the origin of such a staircase structure by
investigating the nature of eigenfunctions closely. It is found that the origin
of the staircase structure could trace back to the anomalous structure in
tunneling tail which manifests itself in the representation using renormalized
action bases. This also explains the reason why the staircase does not appear
in the completely integrable system.
