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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…
Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves…
Motivated by experimental progress in cold atomic systems, we use and advance Localisation Landscape Theory (LLT), to examine two-dimensional systems with point-like random scatterers. We begin by showing that exact eigenstates cannot be…
Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states…
Roughly half of numerical investigations of the Anderson transition are based on consideration of an associated quasi-1D system and postulation of one-parameter scaling for the minimal Lyapunov exponent. If this algorithm is taken…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
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 prove Anderson localization in a disordered photonic crystal waveguide by measuring the ensemble-averaged localization length which is controlled by the dispersion of the photonic crystal waveguide. In such structures, the localization…
We study transport of interacting electrons in a low-dimensional disordered system at low temperature $T$. In view of localization by disorder, the conductivity $\sigma(T)$ may only be non-zero due to electron-electron scattering. For weak…
Stochastic (Anderson) localization is the spatial localization of the wave-function of quantum particles in random media. We show, that a corresponding phenomenon can stabilize spatial solitons in optical resonators: spatial solitons in…
The nature of transport of electrons and classical waves in disordered systems depends upon the proximity to the Anderson localization transition between freely diffusing and localized waves. The suppression of average transport and the…
After exactly half a century of Anderson localization, the subject is more alive than ever. Direct observation of Anderson localization of electrons was always hampered by interactions and finite temperatures. Yet, many theoretical…
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…
We study Anderson localization in two-dimensional systems with purely off-diagonal disorder. Localization lengths are computed by the transfer-matrix method and their finite-size and scaling properties are investigated. We find various…
We study the effect of disorder in a holographic superconductor by introducing a quasi-periodic chemical potential. When the condensation of the superconductor is sufficiently small compared with the strength of disorder, we find that there…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
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…
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 conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al, 1979). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the…
We study the scattering modes of light in a three-dimensional disordered medium, in the scalar approximation and above the critical density for Anderson localization. Localized modes represent a minority of the total number of modes, even…