P Exner et al 2001 J. Phys. A: Math. Gen. 34 9733 doi:10.1088/0305-4470/34/45/312
P Exner1,2, A Joye3 and H Kovarík1,3,4
Show affiliationsWe study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under the 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 that it can have any finite number of open gaps provided that the confining potential is sufficiently strong. However, if W depends on the periodic variable only, we prove by the Thomas argument that the whole spectrum is absolutely continuous, irrespective 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 the Mourre method that a part of the absolutely continuous spectrum persists.
Issue 45 (16 November 2001)
Received 29 June 2001
Published 2 November 2001
P Exner et al 2001 J. Phys. A: Math. Gen. 34 9733
R Balasubramanian et al 2005 Class. Quantum Grav. 22 3015
B R Judd 1980 J. Phys. C: Solid State Phys. 13 2695
S Brian Edgar and José M M Senovilla 2004 Class. Quantum Grav. 21 L133
Ying Cui et al 2007 Phys. Med. Biol. 52 6229
V A Elyukhin et al 2004 J. Phys.: Condens. Matter 16 S2211
Duncan A Brown (for the LIGO Scientific Collaboration) 2005 Class. Quantum Grav. 22 S1097
Robert L P van Veen et al 2005 Phys. Med. Biol. 50 2573
D Morgan et al 1994 J. Phys. G: Nucl. Part. Phys. 20 A1
M Hewitson et al 2007 Class. Quantum Grav. 24 6379