Related papers: Localization for $N$-particle continuous models wi…
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 study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
A conducting 1D line or 2D plane inside (or on the surface of) an insulator is considered.Impurities displace the charges inside the insulator. This results in a long-range fluctuating electric field acting on the conducting line (plane).…
A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A…
Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
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…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…
We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…
We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic,…
We consider the phase coherent transport of a quasi one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow identified in [T. Paul et al., Phys. Rev.…
We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the…
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…
In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Harper model with its quasiperiodic potential shows a transition from extended to localized states. The…
We consider the change in electron localization due to the presence of electron-electron repulsion in the \HA model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an…
We show persistence of both Anderson and dynamical localization in Schr\"odinger operators with non-positive (attractive) random decaying potential. We consider an Anderson-type Schr\"odinger operator with a non-positive ergodic random…
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…
We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens…
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.