相关论文: Some general bounds for 1-D scattering

We consider scattering of a free quantum particle on a singular potential with rather arbitrary shape of the support of the potential. In the classical limit $\hbar=0$ this problem reduces to the well known problem of chaotic scattering.…

In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…

The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…

Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that…

In this paper, we present different proofs of very recent results on the necessary as well as sufficient conditions on the decrease of the potential at infinity for the validity of effective range formulas in 3-D in low energy potential…

Doppler reflectometry spatial and wavenumber resolution is analyzed within the framework of the linear Born approximation in slab plasma model. Explicit expression for its signal backscattering spectrum is obtained in terms of wavenumber…

We point out little discussed phenomenon in elementary quantum mechanics. In one-dimensional potential scattering problems, the scattering amplitudes are not uniquely determined at special points in parameter space. We examine a few…

The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in…

We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…

It is shown that the scattering S-matrix is unitary even if the scattering potential U(x) tends to different limits at plus and minus infinity. This result is in contrast to the statements of some authors which argue that the different…

We present an exact solution to the one-dimensional (1-D) scattering-from-a-barrier problem for an incident neutron described by a wave packet. As an aid to presenting our approach, we spend some time on a basic review of how wave packets…

It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…

In the context of one-dimensional diffusions, we present basic estimates (having the same lower and upper bounds with a factor of 4 only) for four Poincar\'e-type (or Hardy-type) inequalities. The derivation of two estimates have been open…

We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the…

The chaotic scattering theory is here extended to obtain escape-rate expressions for the transport coefficients appropriate for a simple classical fluid, or for a chemically reacting system. This theory allows various transport coefficients…

Scattering on a resonance state coupled to a complicated background is a typical problem for mesoscopic quantum many-body systems as well as for wave propagation in the presence of a complex environment. On average, such a simple mode…

We extend a result on dispersion for solutions of the linear Schr\"odinger equation, proved by Firsova for operators with finitely many energy bands only, to the case of smooth potentials in 1D with infinitely many bands. The proof consists…

The quantum scattering by smooth bodies is considered for small and large values of $kd$, with $k$ the wavenumber and $d$ the scale of the body. In both regimes, we prove that the forward scattering exceeds the backscattering. For high $k$,…

A novel proposal is outlined to determine scattering amplitudes from finite-volume spectral functions. The method requires extracting smeared spectral functions from finite-volume Euclidean correlation functions, with a particular complex…

A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…