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

Pavel Exner (1) , Alain Joye (2)

1 Nuclear Physics Institute [Prague]
2 IF - Institut Fourier

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.

Domaines: Mathématiques [math]; Physique mathématique [math-ph]

Pavel Exner, Alain Joye. Avoided crossings in mesoscopic systems: Electron propagation on a nonuniform magnetic cylinder. Journal of Mathematical Physics, 2001, 42 (10), pp.4707-4738. ⟨hal-01260751⟩