& 50 & 34 & 1/12 & 0.2463 & 0.250\
5 & 50 & 22 & 1/8 & 0.2118 & 0.225\
6 & 50 & 22 & 1/12 & 0.2878 & 0.290\

\[table\]

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Sensitivity of sub-Planck scale structures
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An interesting feature of sub-Planck structures is that they signal the fact that the corresponding quantum state is extremely sensitive to perturbations. We now verify if this holds also for the PT sub-Planck structures found above. Here we consider two different kinds of perturbation: i) an “internal” perturbation, corresponding to a slight change of the PT potential, which is changed from symmetric ($\rho=\kappa$) to a slightly asymmetric one ($\kappa \lesssim \rho$); ii) an “external” perturbation, i.e., a phase-space displacement of the state, for example due to the application of a weak force. As discussed in the preceding section, we consider an initially symmetric PT potential and the compass-like state at the fractional revival time $T_{rev}/8$.

**I.** We set the potential parameter values $\rho=50$, $\kappa=46$ and $\alpha=2\;a.u.$, which give a very small asymmetry (see the solid line in Fig. \[potential\]). We compare this case with the symmetric case $\rho=\kappa=50$. We observe that the small asymmetry does not cause an appreciable modification 