相关论文: Anderson Localization in Euclidean Random Matrices

Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By…

Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson…

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

We survey recent mathematical results about the spectrum of random band matrices. We start by exposing the Erd{\H o}s-Schlein-Yau dynamic approach, its application to Wigner matrices, and extension to other mean-field models. We then…

We study the Anderson localization of atomic gases exposed to three-dimensional optical speckles by analyzing the statistics of the energy-level spacings. This method allows us to consider realistic models of the speckle patterns, taking…

As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…

Anderson localization provides a challenge to numerical approaches due to the inherent randomness, and hence absence of simple symmetries, in its discrete Hamiltonian representation. Numerous algorithmic approaches have been developed or…

We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the…

We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show…

We propose a conceptually new framework to study the onset of Anderson localization in disordered systems. The idea is to expose waves propagating in a random scattering environment to a sequence of short dephasing pulses. The system…

We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in…

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…

We present a thorough study of the complexity of optical localized modes in two-dimensional disordered photonic crystals. Direct experimental measurements of complexity were made using an interferometric setup that allowed for extraction of…

We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…

Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when…

We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are…

This work proposes a very simple random matrix model, the Flip Matrix Model, liable to approximate the behavior of a two dimensional electron in a weak random potential. Its construction is based on a phase space analysis, a suitable…

We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…

Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…

We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at…