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We review recent developments on quantum scattering from mesoscopic systems. Various spatial geometries whose closed analogs shows diffusive, localized or critical behavior are considered. These are features that cannot be described by the…
The scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly…
We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…
We consider the classical self-dual Yang-Mills equation in 3+1-dimensional Minkowski space. We have found an exact solution, which describes scattering of $n$ plane waves. In order to write the solution in a compact form, it is convenient…
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
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.…
When a wave, such as sound or light, scatters within a densely packed particulate, it can be rescattered many times between the particles, which is called multiple scattering. Multiple scattering can be unavoidable when: trying to use sound…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…
Scattering of a scalar particle on a crystalline plane with quadratic cell and identical fixed scatterers is solved precisely. Contradiction of the standard scattering theory is pointed out.
We review and further develop the recently introduced numerical approach for scattering calculations based on a so called pseudo-time Schroedinger equation, which is in turn a modification of the damped Chebyshev polynomial expansion…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…
This report shows formulation of wave scattering in frequency domain. The formulation provides an understanding of S-matrix solver which is named as Scattering Matrix Analyzer (SMatrAn). The S-matrix has the whole of amplitude and phase…