 05251 Hajo Leschke, Simone Warzel, Alexandra Weichlein
 Energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction
(268K, pdf)
Jul 21, 05

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

Abstract. We consider an electrically charged particle on the Euclidean plane subjected to a perpendicular magnetic field which depends only on one
of the two Cartesian coordinates.
For such a ``unidirectionally constant'' magnetic field (UMF), which otherwise may be random or not, we prove certain spectral and transport properties associated with the corresponding oneparticle Schr"odinger operator (without scalar potential) by analysing its ``energyband structure''. In particular, for an ergodic random UMF we provide conditions which ensure that the operator's entire spectrum is almost surely absolutely continuous. This implies that, along the direction in which the random UMF is constant, the quantummechanical motion is almost surely ballistic, while in the perpendicular direction in the plane one has dynamical localisation. The conditions are verified, for example, for Gaussian and Poissonian random UMF's with nonzero meanvalues. These results may be viewed as ``random analogues'' of results first obtained by A. Iwatsuka [Publ. RIMS, Kyoto Univ. 21 (1985) 385] and (nonrigorously) by J. E. M"uller [Phys. Rev. Lett. 68 (1992) 385].
 Files:
05251.src(
05251.keywords ,
lww.pdf.mm )