A Short Course on One-Dimensional Random Schrödinger Operators

Abstract

We discuss various approaches to localization results for one-dimensional random Schrödinger operators, both discrete and continuum. We focus in particular on the approach based on Fürstenberg's Theorem and the Kunz-Souillard method. These notes are based on a series of five one-hour lectures given at University College London in June/July 2011.

31 pages

References in corpus (1)

• Multiscale Analysis and Localization of Random Operators

Cited by in corpus (5)

• Dynamical Localization in Disordered Quantum Spin Systems
• Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent
• Parametric Furstenberg Theorem on Random Products of $SL(2,\mathbb{R})$ matrices
• On the Kunz-Souillard approach to localization for the discrete one dimensional generalized Anderson model
• Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential