Classical and quantum dynamics for 2D-electromagnetic potentials asymptotically homogeneous of degree zero

TL;DR

This paper investigates the classical and quantum behavior of a charged particle in a 2D electromagnetic potential with non-vanishing radial limits, focusing on the dynamics near zeros of the Lorentz force and the associated quantum wave operators.

Contribution

It introduces a detailed analysis of classical and quantum dynamics for potentials with asymptotic homogeneity of degree zero, including the study of wave operator completeness and spiraling states.

Findings

Identification of channels based on zeros of the Lorentz force

Analysis of wave operator completeness in magnetic flux scenarios

Introduction of spiraling states for nonzero magnetic flux

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}.