Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
We consider an electron constrained to move on a surface with revolution symmetry in the presence of a constant magnetic field parallel to the surface axis. Depending on 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.
Keywords
Cite
@article{arxiv.math-ph/0010042,
title = {Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder},
author = {Pavel Exner and Alain Joye},
journal= {arXiv preprint arXiv:math-ph/0010042},
year = {2015}
}