P.Exner, A.Joye, H.Kovarik
Magnetic transport in a straight parabolic channel
(70K, Latex 2e)
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.