Related papers: One-parameter superscaling in three dimensions
Anderson localization marks a halt of diffusive wave propagation in disordered systems. Despite extensive studies over the past 40 years, Anderson localization of light in three dimensions has remained elusive, leading to the question of…
We explore single-particle Anderson localization due to nonrandom quasiperiodic potentials in two and three dimensions. We introduce a class of self-dual models that generalize the one-dimensional Aubry-Andr\'e model to higher dimensions.…
The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is…
We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be…
We study the coarsening dynamics of the three-dimensional random field Ising model using Monte Carlo numerical simulations. We test the dynamic scaling and super-scaling properties of global and local two-time observables. We treat in…
The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and…
We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
The statistics of wavefunctions in the one-dimensional (1d) Anderson model of localization is considered. It is shown that at any energy that corresponds to a rational filling factor f=p/q there is a statistical anomaly which is seen in…
In 1990, Klein, Lacroix, and Speis proved (spectral) Anderson localisation for the Anderson model on the strip of width $W \geqslant 1$, allowing for singular distribution of the potential. Their proof employs multi-scale analysis, in…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
We numerically study the Anderson localization of weekly interacting Bose-Einstein condensate in a one-dimensional disordered potential. We show that two parameters are needed to completely describe such system, and the density profile of…
We discuss the dynamics of particles in one dimension in potentials that are random both in space and in time. The results are applied to recent optics experiments on Anderson localization, in which the transverse spreading of a beam is…
We investigated numerically the distribution of participation numbers in the 3d Anderson tight-binding model at the localization-delocalization threshold. These numbers in {\em one} disordered system experience strong level-to-level…
We use two different fully vectorial microscopic models featuring nonresonant and resonant scattering, respectively, to demonstrate the Anderson localization transition for elastic waves in three-dimensional (3D) disordered solids. Critical…
We develop a self-consistent theoretical approach to the dynamics of Anderson localization in open three-dimensional (3D) disordered media. The approach allows us to study time-dependent transmission and reflection, and the distribution of…
We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the…
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…
We consider a recently proposed model for the propagation of one-photon states in a random medium of two-level atoms. We demonstrate the existence of Anderson localization of single photon states in an energy band centered at the resonant…
We report the first experimental observation of strong multifractality in wave functions at the Anderson localization transition in open three-dimensional elastic networks. Our results confirm the recently predicted symmetry of the…