Pavel Exner, Alain Joye
Avoided crossings in mesoscopic systems: 
electron propagation on a non-uniform magnetic cylinder
(104K, latex)

ABSTRACT.  We consider an electron constrained to move on a 
surface with revolution symmetry in the presence of a constant 
magnetic field $B$ parallel to the surface axis. Depending on $B$ 
and the surface geometry the transverse part of the spectrum 
typically exhibits many crossings which change to avoided 
crossings if a weak symmetry breaking interaction is introduced. 
We study the effect 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 dependent 
Born-Oppenheimer approximation.