WEAK CHAOS IN A QUANTUM KEPLER-PROBLEM

Transition from regular to chaotic dynamics in a crystal made of singu lar scatterers U(r) = lambda\r\(-sigma) can be reached by varying eith er sigma or lambda. We map the problem to a localization problem, and find that in all space dimensions the transition occurs at sigma = 1, i.e., Coulomb potential has marginal singularity. We study the critica l line sigma = 1 by means of a renormalization group technique, and de scribe universality classes of this new transition, An RG equation is written in the basis of. states localized in momentum space. The RG fl ow evolves the distribution of coupling parameters to a universal stat ionary distribution. Analytic properties of the RG equation are simila r to that of Boltzmann kinetic equation: the RG dynamics has integrals of motion and obeys an H-theorem. The RG results for sigma = 1 are us ed to derive scaling laws for transport and to calculate critical expo nents.