Non-adiabatic scattering of a classical particle in an inhomogeneous magnetic field

TL;DR

This paper investigates how a classical electron's motion deviates from adiabatic behavior in a slowly varying magnetic field, providing exact solutions and numerical simulations to understand non-adiabatic scattering effects.

Contribution

It formulates and solves exactly a non-adiabatic scattering problem in inhomogeneous magnetic fields, relevant to composite-fermion theory at half-filled Landau levels.

Findings

Non-adiabatic shift of guiding center is exponentially small.

Shift exhibits oscillatory behavior due to self-commensurability.

Analytical results are supported by numerical simulations.

Abstract

We study the violation of the adiabaticity of the electron dynamics in a slowly varying magnetic field. We formulate and solve exactly a non-adiabatic scattering problem. In particular, we consider scattering on a magnetic field inhomogeneity which models scatterers in the composite-fermion theory of the half-filled Landau level. The calculated non-adiabatic shift of the guiding center is exponentially small and exhibits an oscillatory behavior related to the "self-commensurability" of the drifting cyclotron orbit. The analytical results are complemented with a numerical simulation.