Related papers: Numerical methods for localization
At low temperature, a quasi-one-dimensional ensemble of atoms with attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass…
Spherical localisation is a technique whose history goes back to M.Gromov and V.Milman. It's counterpart, the Euclidean localisation is extensively studied and has been put to great use in various branches of mathematics. The purpose of…
The localization phenomena due to the random potential scattering is widely discussed in the electron and photon systems, where the theoretical approach is the nonlinear $\sigma$ model with the replica method or with the supersymmetry. In…
Anderson localization was discovered 50 years ago to describe the propagation of electrons in the presence of disorder. The main prediction back then, was the existence of disorder induced localized states, which do not conduct electricity.…
The effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…
In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for…
Searching for Anderson localization of light in three dimensions has challenged experimental and theoretical research for the last decades. Here the problem is analyzed through large scale numerical simulations, using a radiative…
Anderson localization is a consequence of coherent interference of multiple scattering events in the presence of disorder, which leads to an exponential suppression of the transmission. The decay of the transmission is typically probed at a…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
Localization is a critical aspect of mobile robotics, enabling robots to navigate their environment efficiently and avoid obstacles. Current probabilistic localization methods, such as the Adaptive-Monte Carlo localization (AMCL) algorithm,…
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,…
This tutorial review gives an overview of the transverse Anderson localization of light in one and two transverse dimensions. A pedagogical approach is followed throughout the presentation, where many aspects of localization are illustrated…
In the present article, we discuss the role played by the interaction in the Anderson localization problem, for a system of interacting fermions in a one-dimensional disordered lattice, described by the Fermi Hubbard Hamiltonian, in…
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…
The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in…
We introduce a new approach for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model at high disorder. In contrast to the usual strategy, we do not study finite…
We investigate Anderson localization of light as occurring in ultra-short excitations. A theory based on time dependent coupled-mode equations predicts universal features in the spectrum of the transmitted pulse. In particular, the process…
Visual place recognition is a fundamental capability for the localization of mobile robots. It places image retrieval in the practical context of physical agents operating in a physical world. It is an active field of research and many…