Random Schrödinger operators and Anderson localization in aperiodic media

@article{RojasMolina2020RandomSO,
  title={Random Schr{\"o}dinger operators and Anderson localization in aperiodic media},
  author={Constanza Rojas-Molina},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
In this note we review some results on localization and related properties for random Schrodinger operators arising in aperiodic media. These include the Anderson model associated to disordered quasycrystals and also the so-called Delone operators, operators associated to deterministic aperiodic structures. 
View PDF on arXiv
1 Citations

One Citation

Citation Type

Citation Type

Localisation for Delone operators via Bernoulli randomisation
Delone operators are Schrodinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given "single-site potential" centred at the points of a…

References

SHOWING 1-10 OF 29 REFERENCES
Random Schr\"odinger Operators on discrete structures
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In…
Spectral properties of disordered systems in the one-body approximation
The paper considers the Schrödinger equation for a single particle and its discrete analogues. Assuming that the coefficients of these equations are homogeneous and ergodic random fields, it is…
Characterization of the Anderson Metal–Insulator Transition for Non Ergodic Operators and Application
We study the Anderson metal–insulator transition for non ergodic random Schrödinger operators in both annealed and quenched regimes, based on a dynamical approach of localization, improving known…
Localization near fluctuation boundaries via fractional moments and applications
We present a short, new, self-contained proof of localization properties of multi-dimensional continuum random Schödinger operators in the fluctuation boundary regime. Our method is based on the…
Absence of Diffusion in Certain Random Lattices
This paper presents a simple model for such processes as spin diffusion or conduction in the "impurity band." These processes involve transport in a lattice which is in some sense random, and in them…
Delone dynamical systems and associated random operators
We carry out a careful study of basic topological and ergodic features of Delone dynamical systems. We then investigate the associated topological groupoids and in particular their representations on…
Ergodicity and dynamical localization for Delone–Anderson operators
We study the ergodic properties of Delone–Anderson operators, using the framework of randomly colored Delone sets and Delone dynamical systems. In particular, we show the existence of the integrated…
Caught by Disorder: Bound States in Random Media
Bound states versus extended states ergodic operator families - definition and abstract theory some important examples our basic models (P+A) and (DIV) localization and Lifshitz tails -the heuristic…
Scale-Free Unique Continuation Estimates and Applications to Random Schrödinger Operators
We prove a unique continuation principle or uncertainty relation valid for Schrödinger operator eigenfunctions, or more generally solutions of a Schrödinger inequality, on cubes of side $${L \in…
A comprehensive proof of localization for continuous Anderson models with singular random potentials
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We…
...
1
2
3
...