Related papers: On non-perturbative Anderson localization for C^\a…
We prove exponential and dynamical localization for the Schr\"odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of…
The purpose of this paper is to understand in more detail the shape of the eigenvectors of the random Schroedinger operator H = Delta+V. Here Delta is the discrete Laplacian and V is a random potential. It is well known that under certain…
We establish large sets of Anderson localized states for the quasi-periodic nonlinear Schr\"odinger equation on $\mathbb Z^d$, thus extending Anderson localization from the linear (cf. Bourgain [Geom. Funct. Anal., 17(3):682--706, 2007]) to…
Proofs of localization for random Schr\"odinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov, or use the classical Wegner estimate as…
For a Hamiltonian ${\hat H}$ containing a position-dependent (disordered) potential, we introduce a sequence of landscape functions $u_n(\vec{r})$ obeying ${\hat H} u_n(\vec{r}) = u_{n-1}(\vec{r})$ with $u_0(\vec{r}) = 1$. For $n \to…
We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length \sigma_R. For speckle potentials the Fourier transform of the…
The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems.
Anderson localization of matter waves was recently observed with cold atoms in a weak 1D disorder realized with laser speckle potential [J. Billy et al., Nature 453, 891 (2008)]. The latter is special in that it does not have spatial…
We present numerical simulations of disordered stealthy hyperuniform layered media ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson…
We present an experimental signature of the Anderson localisation of microcavity polaritons, and provide a systematic study of the dependence on disorder strength. We reveal a controllable degree of localisation, as characterised by the…
We consider a family of self-adjoint operators [H_\omega = - \Delta + \lambda V_\omega, \quad \omega \in \Omega = \bigtimes_{k \in \ZZ^d} \RR,] on the Hilbert space $\ell^2 (\ZZ^d)$ or $L^2 (\RR^d)$. Here $\Delta$ denotes the Laplace…
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…
Anderson localization (AL) phenomena usually exists in systems with random potential. However, disorder-free quantum many-body systems with local conservation can also exhibit AL or even many-body localization transition. In this work, we…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
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 causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator. It is shown that, although this operator does not…
The effect of a weak random potential on two-leg Hubbard ladders is investigated. The random potential is shown to induce Anderson localization except for attractive enough interactions, supressing completely d-wave superconductivity. These…
We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schr\"odinger operators on $\mathbb{Z}^d$ with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on…
In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that…
Anderson localization is a phase transition between a metallic phase, where wavefunctions are extended and delocalized in space, and an insulating phase, where wavefunctions are completely localized. These transitions are driven by…