Classical and quantum dynamics for 2D-electromagnetic potentials asymptotically homogeneous of degree zero
Mathematical Physics
2007-05-23 v1 Dynamical Systems
math.MP
Abstract
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting) Lorentz force (defined for velocities that are purely radial) has a finite number of zeros at fixed energy. Any such zero defines a channel, and to the "stable" ones we associate quantum wave operators. Their completeness is studied in the case of zero as well as nonzero magnetic flux. In the latter case one needs possibly to incorporate a channel of spiraling states. These states are similar to those studied recently in the sign-definite case in \cite {CHS}.
Cite
@article{arxiv.math-ph/0703089,
title = {Classical and quantum dynamics for 2D-electromagnetic potentials asymptotically homogeneous of degree zero},
author = {Horia Cornean and Ira Herbst and Erik Skibsted},
journal= {arXiv preprint arXiv:math-ph/0703089},
year = {2007}
}