Related papers: Multi-particle dynamical localization in a continu…
We consider the multi-particle Anderson tight-binding model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low…
We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results…
We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e.…
Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum…
We consider a continuous one dimensional model of two charged interacting particles in a random potential. The electric repulsion is strictly one dimensional and it inhibits Anderson localization. In fact, the spectrum is continuous. The…
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…
We report a study of three-dimensional (3D) localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed…
At low temperature, a quasi-one-dimensional ensemble of atoms with attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass…
In the present note we show dynamical localization for an Anderson model with missing sites in a discrete setting at the bottom of the spectrum in arbitrary dimension $d$. In this model, the random potential is defined on a relatively dense…
We establish non-perturbative Anderson localization for a wide class of 1D quasiperiodic operators with unbounded monotone potentials, extending the classical results on Maryland model and perturbative results for analytic potentials by…
We consider a system of two discrete quasiperiodic 1D particles as an operator on $\ell^2(\mathbb Z^2)$ and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of…
We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in…
We establish the phenomenon of Anderson localisation for a quantum two-particle system on a d-dimensional lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.
We explore single-particle Anderson localization due to nonrandom quasiperiodic potentials in two and three dimensions. We introduce a class of self-dual models that generalize the one-dimensional Aubry-Andr\'e model to higher dimensions.…
We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…
We give a short summary of the fixed-energy Multi-Scale Analysis (MSA) of the Anderson tight binding model in dimension $d\ge 1$ and show that this technique admits a straightforward extension to multi-particle systems. We hope that this…
This paper revisits the proof of Anderson localization for multi-particle systems. We introduce a multi-particle version of the eigensystem multi-scale analysis by Elgart and Klein, which had previously been used for single-particle…
We discuss the techniques and results of the multi-particle Anderson localization theory for disordered quantum systems with nontrivial interaction. After a detailed presentation of the approach developed earlier by Aizenman and Warzel, we…
In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…
Anderson localization has been observed in various types of waves, such as matter waves, optical waves and acoustic waves. Here we reveal that the effect of Anderson localization can be also induced in metallic nonlinear nanoparticle arrays…