Frédéric Klopp, Michael Loss, Shu Nakamura, Günter Stolz
Oper. Theory Adv. Appl., 224 (2012), 183-219, Jul 3, 2011
We give a detailed survey of results obtained in the most recent half decade<br />
which led to a deeper understanding of the random displacement model, a model<br />
of a random Schr\"odinger operator which describes the quantum mechanics of an<br />
electron in a structurally disordered medium. These results started by<br />
identifying configurations which characterize minimal energy, then led to<br />
Lifshitz tail bounds on the integrated density of states as well as a Wegner<br />
estimate near the spectral minimum, which ultimately resulted in a proof of<br />
spectral and dynamical localization at low energy for the multi-dimensional<br />
random displacement model.