Nonadiabatic scattering of a quantum particle in an inhomogenous magnetic field

We investigate the quantum effects, in particular the Landau-level quantization, in the scattering of a particle the nonadiabatic classical dynamics of which is governed by an adiabatic invariant. As a relevant example, we study the scattering of a drifting particle on a magnetic barrier in the quantum limit where the cyclotron energy is much larger than a broadening of the Landau levels induced by the nonadiabatic transitions. We find that, despite the level quantization, the exponential suppression $\exp(-2\pi d/\delta)$ (barrier width $d$, orbital shift per cyclotron revolution $\delta$) of the root-mean-square transverse displacement experienced by the particle after the scattering is the same in the quantum and the classical regime.