is $0.079\;a.u.$ (see the dotted arrow in Fig. \[plot\]), which is very close to the $x$-span of a sub-Planck structure of the compass-like state, equal to $0.075\;a.u.$, as shown by zoomed view of the Wigner function in the upper inset of Fig. \[plot\]. This means that shifting a single sub-Planck tile results in the cancellation between the positive and negative contributions of the two Wigner functions, thereby making the states quasi-orthogonal.

![(Color online) Plot of the overlap function of Eq. (\[overlap\]) versus the real part of the displacement parameter $\lambda$ (in $a.u.$) at the fractional revival time $T_{rev}/8$ for $\beta=0.4$. Here $\beta^{'}=\tanh |\lambda|\;
e^{i\pi/4}$. The upper inset shows the central interference pattern of the Wigner function and the size of the sub-Planck structures. The lower inset shows an enlarged view of the oscillation for larger $\lambda$. The size of the sub-Planck structure is consistent with the period of oscillation of the overlap.[]{data-label="plot"}](fig7.eps){width="2.7"}

Conclusions
===========

We have shown that sub-Planck scale structures emerge in the time evolution at fractional revival times also in the PT potential. We have studied in particular the generation of compass-like states at $T_{rev}/8$ and benzene-like states at $T_{rev}/12$. We have studied both the symmetric and strongly 