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Theses

Localisation dynamique et égalité des conductances de Hall pour des opérateurs de Schrödinger magnétiques aléatoires

Abstract : The first part of this thesis is devoted to the study of spectral properties of dynamical localization for Schrödinger operators and their classification. We introduce three classes of equivalent properties and investigate the relationships between them in an optimal way. Moreover, some of these properties have been shown to play a crucial role in the mathematical proof of several phenomenon of physical interest such as the quantization of the Hall conductance and the existence of the plateaux due to localized states. Then, we are interested in the bulk and edge Hall conductances for continuous models in the presence of magnetic and electric walls. We explain how the walls come into play in order to define the edge conductance, taking into account the contribution of localized states and the regularization that a disordered media requires. We prove the equality of these conductances by deriving one from the other, and not by separate quantization.
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https://tel.archives-ouvertes.fr/tel-00880091
Contributor : Amal Taarabt <>
Submitted on : Tuesday, November 5, 2013 - 1:17:14 PM
Last modification on : Monday, January 25, 2021 - 2:36:02 PM
Long-term archiving on: : Thursday, February 6, 2014 - 4:36:55 AM

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  • HAL Id : tel-00880091, version 1

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Taarabt Amal. Localisation dynamique et égalité des conductances de Hall pour des opérateurs de Schrödinger magnétiques aléatoires. Physique mathématique [math-ph]. Université de Cergy Pontoise, 2013. Français. ⟨tel-00880091⟩

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