the phase-space area of the tiles is always larger in the case of the benzene-like state; ii) the phase-space area of the tiles *increases* for increasing asymmetry of the PT potential. In the next Section, following the results of [@toscano; @dalvit] we will study the sensitivity to perturbations of the PT sub-Planck structures. One expects to have the highest sensitivity with a state possessing the finest structures in phase space and therefore the above results suggest to choose the compass-like state in the symmetric potential case for this study.

![$Log_e$-$log_e$ plot of the classical action $A$ ($a.u.$) against the area of sub-Planck scale structures ($a$ in $a.u.$) in the Wigner function of the compass-like state for the symmetric PT potential with $\rho=\kappa=50$. The expected scaling law, $a\sim
1/A$, is well verified, since the data are well fitted by the line with slope $-1.02$.[]{data-label="loglog"}](fig4.eps){width="3.in"}

![image](fig5.eps){width="5.2in"}

-.02in

.1in

[|c|c|c|c|c|c|]{} & & & & &\
\[-1.0ex\] & $\rho$ & $\kappa$ & & &\
\[-1.0ex\] & & & $T_{r\!e\!v}$)& &\
1 & 50 & 50 & 1/8 & 0.1084 & 0.110\
2 & 50 & 50 & 1/12 & 0.1420 & 0.144\
3 & 50 & 34 & 1/8 & 0.1278 & 0.132\
4 