Related papers: Some general bounds for 1-D scattering
We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity…
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…
We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of…
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schr\"odinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A…
It is widely assumed in the literature that the specularity parameters for phonon transmission (forward scattering) and reflection (backward scattering) at a boundary are identical, i.e., the statistical distributions of the transition…
We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…
We study the scattering problem, the Sturm-Liouville problem and the spectral problem with periodic or skew-periodic boundary conditions for the one-dimensional Schr\"odinger equation with an $n$-cell (finite periodic) potential. We give…
In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
This thesis describes the development of some basic mathematical tools of wide relevance to mathematical physics. Transmission and reflection coefficients are associated with quantum tunneling phenomena, while Bogoliubov coefficients are…
We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order $2$. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only…
We present a comprehensive method for determining {both exact and approximate} dispersion {relations} for one-dimensional {resonant phononic} crystals, applicable to a wide range of structures, regardless of their specific characteristics.…
Entanglement is usually associated with compound systems. We first show that a one-dimensional (1D) completed scattering of a particle on a static potential barrier represents an entanglement of two alternative one-particle sub-processes,…
We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from…
We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
We present numerical and analytical results for the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. Our mean field analysis identifies regimes where the…