SCATTERING BY AN ULTRALOCAL POTENTIAL IN A NONTRIVIAL TOPOLOGY

Scattering of non-relativistic particles by an ultralocal (delta-) pot ential is considered in two-dimensional manifolds with various topolog y (cylinder, torus, sphere, and Lobachevski plane). The behavior of th e bound state energy as a function of the geometrical and topological characteristics of the space is studied. It is shown that for the comp act non-simply connected manifolds of small radius the variation of th e twisting angles (Aharonov-Bohm fluxes) may lead to delocalization of the bound state. For a simply connected geometry the influence of cur vature on the bound state is considered and the possibility of ''geome tric delocalization'' of the impurity levels is demonstrated explicitl y for the spaces of constant curvature. We also consider the Aharonov- Bohm effect for the anyons on a cylinder. It is shown that a local reg ular potential can induce the Aharonov-Bohm oscillations in the anyon gas with anomalous (non-mesoscopic) dependence of oscillation amplitud e on the geometrical sizes of the system. (C) 1994 Academic Press, Inc .