Related papers: An eigensystem approach to Anderson localization f…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…
In this paper, we prove the Anderson localization near the spectral edge for some alloy-type Anderson-Bernoulli model on $\mathbb{Z}^d$ with exponential long-range hopping. This extends the work of Bourgain [Geometric Aspects of Functional…
We review the theory of multi-particle entanglement. In this book chapter we aim at briefly ``setting the coordinates'' and guiding through the extensive literature in this field. Our coordinate system chosen for this chapter has the axes…
We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of…
We develop the technique to prove localization through the analysis of eigenfunctions in presence of both exponential frequency resonances and exponential phase barriers (anti-resonances) and use it to prove localization for the Maryland…
This short note is a complement to our recent paper [2] where we established strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially…
Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques…
Here I provide additional experimental information and criticise the analysis, modelling, interpretation and claims presented in the recent paper [Nature Communications 11, 4942 (2020)]. I argue that the authors have no clear experimental…
Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov…
As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…
We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…
We establish large sets of Anderson localized states for the quasi-periodic nonlinear wave equation on $\mathbb Z^d$, thus extending nonlinear Anderson localization from the random \cite{BW08} to a deterministic setting.
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…
A new characterization of the Anderson phase transition, based on the response of the system to the boundary conditions is introduced. We change the boundary conditions from periodic to antiperiodic and look for its effects on the…
The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these…
We derive a field-theoretical representation for the moments of the eigenstates in the generalized Anderson model. The representation is exact and can be used for the Anderson model with generic non-random hopping elements in any…
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…
Mathematical analysis of the Anderson localization has been facilitated by the use of suitable fractional moments of the Green function. Related methods permit now a readily accessible derivation of a number of physical manifestations 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…
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…