Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder

TL;DR

This paper investigates how magnetic fields and surface geometry influence electron propagation on a symmetric surface, focusing on avoided crossings and the application of perturbation theory within a quantum dynamical framework.

Contribution

It introduces a reformulation of the problem enabling the use of molecular dynamics tools and develops a perturbation theory for the time-dependent Born-Oppenheimer approximation in this context.

Findings

Analysis of spectral crossings and avoided crossings under magnetic perturbations

Application of molecular dynamics techniques to quantum propagation problems

Development of a perturbation theory for the time-dependent Born-Oppenheimer approximation

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.