Homoclionic and heteroclinic motions in quantum mechanics

Abstract:
Unstable periodic orbits and the associated homoclinic and heteroclinic orbits where shown by Poincare to be the backbone of chaos in classical mechanics. We have recently shown [PRE 70, 35202(R); PRL 94 54101 (2005); PRL 97 94101 (2006); PRL (submitted)] that this important effect has a correspondence in quantum mechanics, thus playing a key role in quantum chaos. Moreover, values for the associated invariant quantized structures (surrogates of homoclinic tori discussed by Ozorio de Almeida) can be extracted solely from the corresponding eigenspectra or quasiprobability quantum density distributions in phase space.