For example, the theorem do not exclude quantum scarring, as the phase space volume of the scars also gradually vanishes in this limit. A quantum eigenstate is scarred by periodic orbit if its probability density is on the classical invariant manifolds near and all along that periodic orbit is systematically enhanced above the classical, statistically expected density along that orbit. In a simplified manner, a quantum scar refers to an eigenstate of whose probability density is enhanced in the neighborhood of a classical periodic orbit when the corresponding classical system is chaotic. In conventional scarring, the responsive periodic orbit is unstable. The instability is a decisive point that separates quantum scars from a more trivial finding that the probability density is enhanced near stable periodic orbits due to the Bohr's correspondence principle. The latter can be viewed as a purely classical phenomenon, whereas in the former quantum interference is important. On the other hand, in the perturbation-induced quantum scarring, some of the high-energy eigenstates of a locally perturbed quantum dot contain scars of short periodic orbits of the corresponding unperturbed system. Even though similar in appearance to ordinary quantum scars, these scars have a fundamentally different origin., In this type of scarring, there are no periodic orbits in the perturbed classical counterpart or they are too unstable to cause a scar in a conventional sense. Conventional and perturbation-induced scars are both a striking visual example of classical-quantum correspondence and of a quantum suppression of chaos (see the figure). In particular, scars are a significant correction to the assumption that the corresponding eigenstates of a classically chaotic Hamiltonian are only featureless and random. In some sense, scars can be considered as an eigenstate counterpart to the quantum ergodicity theorem of how short periodic orbits provide corrections to the universal random matrix theory eigenvalue statistics.