Related papers: Exponential decay of scattering coefficients
The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to learn more about this process, we carry out discrete element simulations of the system response to excitations…
We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time \pi on…
Besides the unitarity and symmetry requirements for a multi-resonance scattering amplitude, several other natural conditions can easily exclude unrealistic proposals. In particular, the behaviour of singularities under the variation of…
The transmission characteristics of a spherical (possibly multilayered) particle of arbitrary size under focused illumination are discussed within the generalized Lorenz-Mie theory. Expressions generalizing the total extinction and…
This paper presents the analysis and characterization of the surface scattering process for both specular and diffused components. The study is focused on the investigation of various building materials each having a different roughness, at…
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…
We investigate the high-energy behavior of the elastic scattering amplitude using the eikonal and $U$-matrix unitarization schemes. This work extends the analysis in [1] by exploring the sensitivity of the Pomeron and Odderon parameters to…
The energy extinction cross section of a concentrically layered sphere varies with velocity as the Doppler shift moves the spectral content of the incident signal in the sphere's co-moving inertial reference frame toward or away from…
We investigate the spectral and eigenstate properties of the quantum superexponential oscillator. Our focus is on the quantum signatures of the recently observed transition of the energy dependent period of the corresponding classical…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its…
An explicitly crossing-symmetric decomposition of the pion-pion scattering amplitudes into low- and high-energy components is established. The high-energy components are entirely determined by absorptive parts at high energies. With the…
We consider spherical averages of the Fourier transform of fractal measures and improve both the upper and lower bounds on the rate of decay. Maximal estimates with respect to fractal measures are deduced for the Schr\"odinger and wave…
High-energy factorization in QCD is investigated beyond leading order and its relationship to the factorization theorem of mass singularities is established to any collinear accuracy. Flavour non-singlet observables are shown to be regular…
We prove decay with respect to some Lebesgue norms for a class of Schr\"odinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space…
3D Compton scattering imaging is an upcoming concept exploiting the scattering of photons induced by the electronic structure of the object under study. The so-called Compton scattering rules the collision of particles with electrons and…
Statistics of many particle energy levels of a finite two-dimensional system of interacting electrons is numerically studied. It is shown that the statistics of these levels undergoes a Poisson to Wigner crossover as the strength of the…
I discuss elastic dipole-dipole scattering in QCD at high energies, with emphasis on the relation between Mueller's dipole picture and the Color Glass Condensate, and on the importance of rare fluctuations for the high-energy limit of the…
We analytically study the time-averaged electromagnetic energy stored inside scatterers containing inclusions of arbitrary shapes. Assuming the low density of inclusions, we derive the expression for the energy-transport velocity through…
We consider a noncoherent wireless network, where the transmitters and receivers are cognizant of the statistics of the fading coefficients, but are ignorant of their realizations. We demonstrate that if the nodes do not cooperate, if they…