Abstract. We study the ergodic properties of Delone-Anderson opera-tors, using the framework of randomly coloured Delone sets and Delone dynamical systems. In particular, we show the existence of the inte-grated density of states and, under some assumptions on the geometric complexity of the underlying Delone sets, we obtain information on the almost-sure spectrum of the family of random operators. We then ex-ploit these results to study the Lifshitz-tail behaviour of the integrated density of states of a Delone–Anderson operator at the bottom of the spectrum. This is used as an input for the multi-scale analysis to prove dynamical localization. We also estimate the size of the spectral region where dynamical localization occurs. 1
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson mod...
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This book provides an introduction to the mathematical theory of disorder effects on quantum spectra...
AbstractIn this paper we study localization for ergodic families of discrete Schrödinger operators. ...
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson mod...
We give a proof of exponential localization in the Anderson model with long range hopping based on a...
We give a simple geometric proof of Wegner's estimate which leads to a variety of new results o...
Abstract. We show persistence of both Anderson and dynamical local-ization in Schrödinger operators...
Abstract. We prove that, for a general class of random operators, the family of the unfolded eigenva...
AbstractWe prove the existence with probability one of an interval of pure point spectrum for some f...
We prove spectral and dynamical localization for the multi-dimensional random displace-ment model ne...
We prove spectral and dynamical localization for a one-dimensional Dirac operator to which is added ...
I consider random Schrödinger operators with exponentially decaying single site potential, which is...
Abstract. We study the Anderson metal-insulator transition for non ergodic random Schrdinger operato...
We consider a random Schrödinger operator on the binary tree with a random potential which is the su...
ABSTRACT. We consider Schrödinger operators on L 2 (R d) with a random potential concentrated near t...
We study the breaking of ergodicity measured in terms of return probability in the evolution of a qu...
This book provides an introduction to the mathematical theory of disorder effects on quantum spectra...
AbstractIn this paper we study localization for ergodic families of discrete Schrödinger operators. ...
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson mod...
We give a proof of exponential localization in the Anderson model with long range hopping based on a...
We give a simple geometric proof of Wegner's estimate which leads to a variety of new results o...