Browsing by Author "Germinet, Francois"

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    Quantization of Edge Currents along Magnetic Barriers and Magnetic Guides
    (2011) Dombrowski, Nicolas; Germinet, Francois; Raikov, Georgi
    We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized Iwatsuka potentials. In both cases, we prove quantization of the edge conductance. Next, we consider magnetic perturbations of such magnetic barriers or guides and prove stability of the quantized value of the edge conductance. Further, we establish a sum rule for edge conductances. Regularization within the context of disordered systems is discussed as well.
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    Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media
    (2010) Dombrowski, Nicolas; Germinet, Francois; Raikov, Georgi
    In this paper we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical delocalization near the center of the band in the sense that wave packets travel at least at a given minimum speed. We provide explicit examples of magnetic perturbations that split the Landau levels into full intervals of spectrum.