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Linear response theory for magnetic Schrödinger operators in disordered media |
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| Authors: | Jean-Marc Bouclet Jeffrey H Schenker |
| Institution: | a Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d’Ascq Cédex, France b Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France c Department of Mathematics, University of California, Irvine, Irvine, CA 92697-3875, USA d Theoretische Physik, ETH, CH-8093 Zürich, Switzerland |
| Abstract: | We justify the linear response theory for an ergodic Schrödinger operator with magnetic field within the noninteracting particle approximation, and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the Fermi level falls into a region of localization, we recover the well-known Kubo-Str?eda formula for the quantum Hall conductivity at zero temperature. |
| Keywords: | primary 82B44 secondary 47B80 60H25 |
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