Related papers: The repulsion between localization centers in the …
As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\bf Z}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence strong…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…
We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger…
We explore the properties of discrete random Schroedinger operators in which the random part of the potential is supported on a sub-lattice. In particular, we provide new conditions on the sub-lattice under which Anderson localisation…
We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…
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 prove that, for a density of disorder $\rho$ small enough, a certain class of discrete random Schr\"odinger operators on $\Z^d$ with diluted potentials exhibits a Lifschitz behaviour from the bottom of the spectrum up to energies at a…
We analyze the conductance distribution function in the one-dimensional Anderson model of localization, for arbitrary energy. For energy at the band center the distribution function deviates from the universal form assumed in…
Localization results for a class of random Schr\"odinger operators within the Hartree-Fock approximation are proved in two regimes: large disorder and weak disorder/extreme energies. A large disorder threshold $\lambda_{\mathrm{HF}}$…
For the multi-particle Anderson model with correlated random potential in the continuum, we show under fairly general assumptions on the inter-particle interaction and the random external potential, the Anderson localization which consists…
We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply-peaked quasi-extended modes.…
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…
In this paper we review results of Anderson localization for different random families of operators which enter in the framework of random quasi-one-dimensional models. We first recall what is Anderson localization from both physical and…
We consider Schr\"odinger operators in $\ell^2(\Z)$ whose potentials are obtained by randomly concatenating words from an underlying set $\mathcal{W}$ according to some probability measure $\nu$ on $\mathcal{W}$. Our assumptions allow us to…
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded…
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 prove Anderson localization at the internal band-edges for periodic magnetic Schr{\"o}dinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of…