Classical Motions in Quantum Mechanics

After the pioneering work of Poincare, Lorenz and others
we have a clear definition of chaos at the clssical level.
On the other hand, a similar definition for the realm of
the quantum world has always shown elusive.
There are however some well established manifestations of
chaotic bahavior in quantum mechanics, something defined
by Berry as 'quantum chaology'.
Among them the universal properties in the spectra of
classical chaotic systems shown by Bohigas, Gutzwiller's
trace formulae for the quantization of such systems in
terms of periodic orbits, or the scar theory developed by
Heller, deserve special mention.
Recently, we have shown that the homoclinic and heteroclinic
motions, two of the key elements used by Poincare to
understand Hamiltonian classical chaos leave also a
unmistakeable signature in quantum dynamics [1,2,3,4].

[1] Wisniacki, Vergini, Benito, and Borondo, Phys. Rev. E 70, 035202(R) (2004).
[2] Wisniacki, Vergini, Benito, and Borondo, Phys. Rev. Lett. 94, 054101 (2005).
[3] Wisniacki, Vergini, Benito, and Borondo, Phys. Rev. Lett. 97, 094101 (2006).
[4] Sibert, Vergini, Benito, Borondo, New J. Phys. 10, 053016 (2008).