Related papers: Large-scale dispersive estimates for acoustic oper…
This is a complement to our earlier work \cite{C10a} where a new eigenvalue concentration bound for multi-particle disordered quantum lattice systems was obtained. Here we show that the new bound leads to a simplified proof of…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
We prove that a strong form of dynamical localization follows from a variable energy multi-scale analysis. This abstract result is applied to a number of models for wave propagation in disordered media.
Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…
This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusions of brine and air. From a pulse emitted by a source above…
We show absence of energy levels repulsion for the eigenvalues of random Schr\"odinger operators in the continuum. We prove that, in the localization region at the bottom of the spectrum, the properly rescaled eigenvalues of a continuum…
We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator.…
Do nonlinear waves destroy Anderson localization? Computational and experimental studies yield subdiffusive nonequilibrium wave packet spreading. Chaotic dynamics and phase decoherence assumptions are used for explaining the data. We…
We consider acoustic waves propagating in an inviscid fluid interacting with a rigid periodically perforated plate in the presence of permanent flows. The paper presents a model of an acoustic interface obtained by the asymptotic…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally…
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…
This paper concerns the numerical approximation of low-energy eigenstates of the linear random Schr\"odinger operator. Under oscillatory high-amplitude potentials with a sufficient degree of disorder it is known that these eigenstates…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results…
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the statistical instability of the wave energy…
Using a cutoff-free formulation of the coherent transport theory, we show that the interference terms at the origin of localization strongly affect the transport anisotropy. In contrast to the common hypothesis, we then find that the…
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 propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…