Non-adiabatic 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 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. 
F. Evers, A. D. Mirlin, D. G. Polyakov, and P. Woelfle