Related papers: Nonlinear Anderson localized states at arbitrary d…
We consider a two dimensional magnetic Schroedinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate…
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 study effects of a bounded and compactly supported perturbation on multi-dimensional continuum random Schr\"odinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schr\"odinger…
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 suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the…
In this paper, we study quasi-periodic CMV matrices with Verblunsky coefficients given by the skew-shift. We prove the positivity of Lyapunov exponents and Anderson localization for most frequencies, which establish the analogous results of…
The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization.…
We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear…
The one-dimensional (1d) Anderson model (AM) has statistical anomalies at any rational point $f=2a/\lambda_{E}$, where $a$ is the lattice constant and $\lambda_{E}$ is the de Broglie wavelength. We develop a regular approach to anomalous…
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…
In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible…
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,…
In this paper, we consider the Schr\"{o}dinger operators on $ \ell^{2}(\N) $, defined for all $ x\in\mathbb{T} $ by \begin{equation} (H(x)u)_n = u_{n+1} + u_{n-1} + \lambda f(2^{n} x) u_n, \quad \text{for } n \geq 0,\notag \end{equation}…
We first study the discrete Schr\"odinger equations with analytic potentials given by a class of transformations. It is shown that if the coupling number is large, then its logarithm equals approximately to the Lyapunov exponents. When the…
We establish Anderson localization for 1-d discrete Schr\"odinger operators with positive weights. The distinctive feature of this work lies in the degeneracy of the weights, with both the potentials and weights assumed to be analytic and…
We consider a random Schr\"odinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, $Q_r$, and a random transversally periodic potential, $\kappa Q_t$, with coupling constant…
We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the…
The four-wave interaction in quantum nonlinear Schr\"odinger lattices with disorder is shown to destroy the Anderson localization of waves, giving rise to unlimited spreading of the nonlinear field to large distances. Moreover, the process…
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…
1D diagonally disordered chain with Frenkel exciton and long range exponential intersite interaction is considered. It is shown that some states of this disordered system are delocalised (extended) contrary to the popular statement that all…