Related papers: Self-averaging of Wigner transforms in random medi…
We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…
We show that when Brownian motion takes place in a heterogeneous medium, the presence of local forces and transport coefficients leads to deviations from a Gaussian probability distribution that make that the ratio between forward and…
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…
We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small…
The entanglement between two arbitrary subsystems of random pure states is studied via properties of the density matrix's partial transpose, $\rho_{12}^{T_2}$. The density of states of $\rho_{12}^{T_2}$ is close to the semicircle law when…
An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form…
In this article we reconsider the problem of the propagation of waves in a random medium in a kinetic regime. The final aim of this program would be the understanding of the conditions which allow to derive a kinetic or radiative transfer…
We study diffusion in a network which is governed by non-autonomous Kirchhoff conditions at the vertices of the graph. Also the diffusion coefficients may depend on time. We prove at first a result on existence and uniqueness using form…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being i.i.d. random variables with mean zero and unit variance. We additionally suppose that $\mathbb E |X_{11}|^{4 + \delta} =:…
This work is devoted to the asymptotic analysis of high frequency wave propagation in random media with long-range dependence. We are interested in two asymptotic regimes, that we investigate simultaneously: the paraxial approximation,…
The Wigner delay is defined as the energy derivative of the scattering phase of a particle in a given potential, unveiling the time taken (or gained) due to the interaction. The characterisation of this delay plays a central role in…
Motivated by recent experiments, we consider a Schr\"{o}dinger cat superposition of two widely separated coherent states in thermal equilibrium. The time development of our system is obtained using Wigner distribution functions. In contrast…
Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under…
The Wigner time delay of slow particles in the process of their elastic scattering by complex targets formed by several zero-range potentials is investigated. It is shown that at asymptotically large distances from the target, the…
We consider the propagation of two-photon light in a random medium. We show that the Wigner distribution of the two-photon wave function obeys an equation that is analogous to the radiative transport equation for classical light. Using this…
The concept of superbandwidth refers to the fact that a band-limited signal can exhibit, locally, an increase of its bandwidth, i.e., an effective bandwidth greater than that predicted by its Fourier transform. In this work, we study the…
The spectral decomposition of the elastic wave operator in a layered isotropic half-space is derived by means of standard functional analytic methods. Particular attention is paid to the coupled $P$-$SV$ waves. The problem is formulated…
The transmission problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. After four decades of research motivated by scattering theory, the spectral properties of this…
Under certain circumstances, Voigt waves can propagate in a biaxial composite medium even though the component material phases individually do not support Voigt wave propagation. This phenomenon is considered within the context of the…