Related papers: Localization for one-dimensional random potentials…
We study localized two- and three-dimensional Langmuir solitons in the framework of model based on generalized nonlinear Schr\"odinger equation that accounts for local and nonlocal contributions to electron-electron nonlinearity. General…
The realization that electron localization in disordered systems (Anderson localization) is ultimately a wave phenomenon has led to the suggestion that photons could be similarly localized by disorder. This conjecture attracted wide…
Here we study novel effects associated with electromagnetic wave propagation in a Robertson-Walker universe and the Schwarzschild spacetime with a small amount of metric stochasticity. We find that localization of electromagnetic waves…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
We evaluate the localization length of the wave (or Schroedinger) equation in the presence of a disordered speckle potential. This is relevant for experiments on cold atoms in optical speckle potentials. We focus on the limit of large…
The weak localization correction and the mesoscopic fluctuations of the polarizability and the capacitance of a small disordered sample are studied systematically in 2D and 3D geometries. While the grand canonical ensemble calculation gives…
We study the homogenization of a Schr\"{o}dinger equation in a locally periodic medium. For the time and space scaling of semi-classical analysis we consider well-prepared initial data that are concentrated near a stationary point (with…
We discuss various approaches to localization results for one-dimensional random Schr\"odinger operators, both discrete and continuum. We focus in particular on the approach based on F\"urstenberg's Theorem and the Kunz-Souillard method.…
We perform a detailed numerical study of the conductance $G$ through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies $\epsilon$ of the tight-binding Hamiltonian are…
This paper investigates the localization properties of solutions to the semi-classical Schr\"odinger equation on closed Riemann surfaces. Unlike classical studies that assume a smooth potential, our work addresses the challenges arising…
We study the statistics of Dirichlet eigenvalues of the random Schr\"odinger operator $-\epsilon^{-2}\Delta^{(\text{d})}+\xi^{(\epsilon)}(x)$, with $\Delta^{(\text{d})}$ the discrete Laplacian on $\mathbb Z^d$ and $\xi^{(\epsilon)}(x)$…
We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition…
We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a…
In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the…
We review various formulations of conductivity for one-particle Hamiltonians and relate them to the current-current correlation measure. We prove that the current-current correlation measure for random Schr\"odinger operators has a density…
Applying the method of characteristics leads to wavefunctions and dynamic localization conditions for electrons on the one dimensional lattice under perpendicular time dependent electric and magnetic fields. Such conditions proceed again in…
We study the localization of eigenfunctions produced by a point scatterer on a thin rectangle. We find an explicit set of eigenfunctions localized to part of the rectangle by showing that the one-dimensional Schr\"odinger operator with a…
One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new…
We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the…
We study localization and delocalization in a class of non-hermitean Hamiltonians inspired by the problem of vortex pinning in superconductors. We show how to take into account multiple scattering. We also obtain some bounds on the complex…