Related papers: Non-stationary Anderson Localization
We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The potentials are located on a randomly distorted lattice…
We prove long time Anderson localization for nonlinear random Schroedinger equation in $\ell^2$ by making a Birkoff normal form type transform to creat an energy barrier where there is essentially no mode propagation. One of the new…
The perturbation theory is developed for joint statistics of the advanced and retarded Green's functions of the 1D Schrodinger equation with a piecewise-constant random potential. Using this method, analytical expressions are obtained for…
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 investigate the equivalence between dynamical localization and localization properties of eigenfunctions of Schr\"odinger Hamiltonians. We introduce three classes of equivalent properties and study the relationships between them. These…
We present an eigensystem multiscale analysis for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model in an energy interval. In particular, it yields…
For the nonlinear Schreodinger equation (NLSE), in presence of disorder, exponentially localized stationary states are found. In the present Letter it is demonstrated analytically that the localization length is typically independent of the…
We consider continuous one-dimensional multifrequency Schr\"odinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine…
We study location of eigenvalues of one-dimensional discrete Schr\"odinger operators with complex $\ell^{p}$-potentials for $1\leq p\leq \infty$. In the case of $\ell^{1}$-potentials, the derived bound is shown to be optimal. For $p>1$, two…
For the Nonlinear Shr\"odinger Equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear…
The phenomenon of Anderson localization is studied for a class of one-particle Schr\"odinger operators with random Zeeman interactions. These operators arise as follows: Static spins are placed randomly on the sites of a simple cubic…
The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schr\"{o}dinger equations mainly the compactness of the support and its spatial localization. This question is very related with pure…
The wave function of a non-relativistic particle in a periodic potential admits oscillatory solutions, the Bloch waves. In the presence of a random noise contribution to the potential the wave function is localized. We outline a new proof…
We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice…
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 consider a class of unbounded quasiperiodic Schr\"odinger-type operators on $\ell^2(\mathbb Z^d)$ with monotone potentials (akin to the Maryland model) and show that the Rayleigh--Schr\"odinger perturbation series for these operators…
We consider the multi-particle Anderson model on the lattice with infinite range but sub-exponentially decaying interaction and show the Anderson localization consisting of the spectral exponential and the strong dynamical localization. In…
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In these notes we give a review of the…
We study localization and derive stochastic estimates (in particular, Wegner and Minami estimates) for the eigenvalues of weakly correlated random discrete Schr\"odinger operators in the localized phase. We apply these results to obtain…
We prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed…