相关论文: Transmission eigenvalues for multipoint scatterers

In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff--Love infinite plate problem.…

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…

Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission…

We develop the d-bar -approach to inverse scattering at zero energy in dimensions d>=3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction…

Our study of the evolution of transmission eigenvalues, due to changes in various physical parameters in a disordered region of arbitrary dimensions, results in a generalization of the celebrated DMPK equation. The evolution is shown to be…

We study electron propagation through a random array of rare, opaque and large (compared the de Broglie wavelength of electrons) scatterers. It is shown that for any convex scatterer the ratio of the transport to quantum lifetimes…

Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a…

We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral…

Several integral identities related to acoustic scattering are presented. In each case the identity involves the integral over frequency of a physical quantity. For instance, the integrated transmission loss, a measure of the transmitted…

We develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a…

We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…

We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at low density. The positive Lyapunov exponent may be obtained either by a direct analysis of the dynamics, or by the use of kinetic theory methods. To leading orders…

The interior transmission eigenvalue problem (ITP) plays a central role in inverse scattering theory and in the spectral analysis of inhomogeneous media. Despite its smooth dependence on the refractive index at the PDE level, the…

We consider the distribution of the transmission coefficients, i.e. the singular values of the modal transmission matrix, for 2D random media with periodic boundary conditions composed of a large number of point-like non-absorbing…

Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…

We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by $U(2)\times U(2)$, which is described by eight real parameters. We…

Positive recurrence of a $d$-dimensional diffusion with switching and with one recurrent and one transient regimes and variable switching intensities is established under suitable conditions. The approach is based on embedded Markov chains.

Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the…

We numerically investigate the Anderson transition in an effective dimension $d$ ($3 \leq d \leq 11$) for one particle propagation in a model random and quasiperiodic potential. The found critical exponents are different from the standard…

We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions.…