Related papers: Wegner bounds for one-dimensional multi-particle B…

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

We prove localization at the bottom of the spectrum for a random Schr\"odinger operator in the continuum with a single-site potential probability distribution supported by a Cantor set of zero Lebesgue measure. This distribution is too…

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…

We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and…

We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…

We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple…

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…

This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the…

Unlike many particle systems, Activated Random Walk has nontrivial behavior even in one spatial dimension. We prove inner and outer bounds on the spread of n activated random walkers from a single source in Z. The inner bound involves a…

We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…

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 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 study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis we prove exponential and strong dynamical localization of any order in the Hilbert-Schmidt norm near the spectral edge. Apart from the…

The localization properties of eigenfunctions for two interacting particles in the one-dimensional Anderson model are studied for system sizes up to $N=5000$ sites corresponding to a Hilbert space of dimension $\approx 10^7$ using the Green…

We study the transport of an interacting Bose--Einstein condensate through a 1D correlated disorder potential. We use for this purpose the truncated Wigner method, which is, as we show, corresponding to the diagonal approximation of a…

approaches. We demonstrate that the Wigner regime can be reached using small values of the confinement parameter. To obtain physical insight in our results we analyze them with a semi-analytical model for two electrons. Thanks to…

The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…

We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely…

We consider long-range correlated disorder and mutual interacting particles according to a dipole-dipole coupling as modifications to the one-dimensional Anderson model. Technically we rely on the (numerical) exact diagonalization of the…

We establish exponential localization for a multi-particle Anderson model in a Euclidean space of an arbitrary dimension, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we…