asymmetric PT potential and we have verified that in all cases the phase-space area of the sub-Planck structures scales as $\hbar^2/A$, where $A$ is the classical action associated with the state. In particular we have seen the smallest phase-space structure (‘tile’) is associated with that of the compass-like state of the symmetric PT potential. For this reason we have considered this state for analyzing the sensitivity of the PT system to perturbations. We have considered the effect on this state of a slight asymmetry of the potential and of a phase-space displacement. We have seen that in both cases, the sub-Planck structures are responsible for high sensitivity, because as soon as a single tile is displaced in phase space so that its maximum coincides with a minimum of the undisplaced state, one has destructive interference and the two states become approximately orthogonal.

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