01-111 P.Exner, A.Joye, H.Kovarik

Magnetic transport in a straight parabolic channel (70K, Latex 2e) Mar 26, 01

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We study a charged two-dimensional particle confined to straight parabolic-potential channel and exposed to a homogeneous magnetic field under influence of a potential perturbation $W$. If $W$ is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any finite number of open gaps provided the confining potential is sufficiently strong. However, if $W$ depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if $W$ is small and satisfies a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists.

Files: 01-111.src( 01-111.keywords , parabol.tex )