Avoided crossings in mesoscopic systems: Electron propagation on a nonuniform magnetic cylinder

We consider an electron constrained to move on a surface with revolution sy mmetry in the presence of a constant magnetic field B parallel to the surfa ce axis. Depending on B and the surface geometry the transverse part of the spectrum typically exhibits many crossings which change to avoided crossin gs if a weak symmetry breaking interaction is introduced. We study the effe ct of such perturbations on the quantum propagation. This problem admits a natural reformulation to which tools from molecular dynamics can be applied . In turn, this leads to the study of a perturbation theory for the time de pendent Born-Oppenheimer approximation. (C) 2001 American Institute of Phys ics.