# Localization and eigenvalue statistics for the lattice Anderson model with discrete disorder

@article{Imbrie2017LocalizationAE, title={Localization and eigenvalue statistics for the lattice Anderson model with discrete disorder}, author={John Z. Imbrie}, journal={arXiv: Mathematical Physics}, year={2017} }

We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.

## 5 Citations

### Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice

- MathematicsInventiones mathematicae
- 2019

We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent…

### Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice

- MathematicsInventiones mathematicae
- 2019

We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent…

### Spectral properties of localized continuum random Schrödinger operators

- Mathematics
- 2018

The results presented in this thesis are mainly motivated by the attempt to improve the mathematical understanding of the localized spectral region of random quantum mechanical systems. It is common…

### Topology and Localization: Mathematical Aspects of Electrons in Strongly-Disordered Media

- Physics, Mathematics
- 2018

Topological insulators are usually studied in physics under the assumption of translation invariance, which allows for the usage of Bloch decomposition. Mathematically vector bundle theory over the…

### Time evolution of many-body localized systems in two spatial dimensions

- PhysicsPhysical Review B
- 2020

Many-body localization is a striking mechanism that prevents interacting quantum systems from thermalizing. The absence of thermalization behaviour manifests itself, for example, in a remanence of…

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We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent…

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