Understanding the Random Displacement Model: From Ground-State Properties to Localization
Abstract
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.
Cite
@article{arxiv.1107.0386,
title = {Understanding the Random Displacement Model: From Ground-State Properties to Localization},
author = {Frédéric Klopp and Michael Loss and Shu Nakamura and Günter Stolz},
journal= {arXiv preprint arXiv:1107.0386},
year = {2018}
}
Comments
31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 2010