Related papers: From fixed-energy MSA to dynamical localization: A…
We characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of…
We prove dynamical and spectral localization at all energies for the discrete generalized Anderson model via the Kunz-Souillard approach to localization. This is an extension of the original Kunz-Souillard approach to localization for…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We consider discrete Schr\"odinger operators on $\ell^2(\mathbb{Z})$ with bounded random but not necessarily identically distributed values of the potential. We prove spectral localization (with exponentially decaying eigenfunctions) as…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
Based on the statistical dynamical mean field theory, we investigate, in a generic model for a strongly coupled disordered electron-phonon system, the competition between polaron formation and Anderson localization. The statistical…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized…
A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution…
The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schr\"odinger operators in the continuum. One of…
This work establishes the Anderson localization in both the spectral exponential and the strong dynamical localization for the multi-particle Anderson tight-binding model with correlated but strongly mixing random external potential. The…
For Anderson Localization models with multifractal eigenvectors on disordered samples containing $N$ sites, we analyze in a unified framework the consequences for the statistical properties of the Green function. We focus in particular on…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…
We prove a connection between the Green's function of the fractional Anderson model and the two point function of a self-avoiding random walk with long range jumps, adapting a strategy proposed by Schenker in 2015. This connection allows us…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical…
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are…
Solving the single-impurity Anderson model (SIAM) is a basic problem of solid state physics. The SIAM model is very important, at present it is also used for systems with quantum impurities, e.g. semiconductor quantum dots and molecular…
We consider the multi-particle Anderson model on the lattice with infinite range but sub-exponentially decaying interaction and show the Anderson localization consisting of the spectral exponential and the strong dynamical localization. In…
We use time-dependent spin-density-functional theory to study dynamical magnetic phenomena. First, we recall that the local-spin-density approximation (LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic state of…