Nonadiabatic scattering of a quantum particle in an inhomogenous magnetic field

¹ Ecole Doctorale de Physique, Université Joseph Fourier Grenoble 1, 38042 Grenoble, France
² Institut für Nanotechnologie, Forschungszentrum Karlsruhe 76021 Karlsruhe, Germany
³ Institut für Theorie der Kondensierten Materie, Universität Karlsruhe 76128 Karlsruhe, Germany

Received: 29 January 2001
Accepted: 20 June 2001

Abstract

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 (barrier width d, orbital shift per cyclotron revolution δ) of the root-mean-square transverse displacement experienced by the particle after the scattering is the same in the quantum and the classical regime.