Energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction

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dc.creatorLeschke, Hajo
dc.creatorWarzel, Simone
dc.creatorWeichlein, Alexandra
dc.date2005-07-15
dc.date.accessioned2026-07-07T06:27:12Z
dc.date.available2026-07-07T06:27:12Z
dc.descriptionWe consider an electrically charged particle on the Euclidean plane subjected to a perpendicular magnetic field which depends only on one of the two Cartesian co-ordinates. 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 one-particle Schroedinger operator (without scalar potential) by analysing its ``energy-band 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 quantum-mechanical 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 non-zero mean-values. These results may be viewed as ``random analogues'' of results first obtained by A. Iwatsuka [Publ. RIMS, Kyoto Univ. 21 (1985) 385] and (non-rigorously) by J. E. Mueller [Phys. Rev. Lett. 68 (1992) 385].
dc.identifierhttps://arxiv.org/abs/math-ph/0507035
dc.identifierhttp://arxiv.org/abs/math-ph/0507035
dc.identifierAnnales Henri Poincare 7 (2006) 335-363
dc.identifierdoi:10.1007/s00023-005-0251-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97347
dc.subjectMathematical Physics
dc.subjectDisordered Systems and Neural Networks
dc.titleEnergetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction
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