Nonadiabatic scattering of a classical particle in an inhomogeneous magnetic field

We study the violation of the adiabaticity of the electron dynamics in a slowly varying magnetic field. We formulate and solve exactly a nonadiabatic scattering problem. In particular, we consider scattering on a magnetic field inhomogeneity that models scatterers in the composite-fermion theory of the half-filled Landau level. The calculated nonadiabatic 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