Yo, I am the author of this paper
http://arxiv.org/abs/cond-mat/9704118
back in the day. At that time Albert Sievers at Cornell was very interested in the question of localization, connected with this idea that was called "two-level systems".
Anyway when we are talking about classical mechanics, localization is easy to find. The trouble is finding it in real systems and in quantum mechanical theory.
Here is an idea I talked about with Al but it never went anywhere.
Back in the old days with the Bohr Atom you had the amount of "action" that was quantized like (n+1/2) hbar. In the case of an anharmonic localized exception there are two things to think about at the semiclassical limit. When I was working with Al's group one could differentiate between the "periodic orbit" which the core of the anon, vs. the excitations around that periodic orbit. In the paper above the situation was constrained such that a single momentum-position manifold exists to leak out of the anon mode.
The nexts step, which we never did, would be to try the simulation with a realistic potential AND check if (1) we couid make an anon with (n+1/2) hbar worth of action, and (2) if the stable region around the anon has a surface area < hbar. If (1) and (2) are both the case the classical version has some validity, but if they are not true, the graininess of quantum mechanics would make the anon state impossible to find. That's my take.