Related papers: Analytic bounds on transmission probabilities
The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two…
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…
A method to compute the scattering solutions of a spinless Salpeter equation (or a Schrodinger equation) with a central interaction is presented. This method relies on the 3-dimensional Fourier grid Hamiltonian method used to compute bound…
We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger…
The paper discusses the applicability of WKB and Born (small perturbations) approximations in the problem of the backscattering of quantum particles and classical waves by one-dimensional smooth potentials with amplitudes small compared to…
How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints? In applications, state constraints may encode safety…
The method of potential envelopes is used to analyse the bound-state spectrum of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the…
Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…
We obtain general bounds on scattering processes involving charged particles in 1+1 spacetime dimensions. After a general analysis we derive mostly numerical bounds on couplings in theories with $O(N)$ and $U(N)$ global symmetries. The…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
By applying continuity and boundary conditions, the reflection and transmission coefficients of one-dimensional time-independent Schr\"odinger equation with a symmetric barrier-type shifted Deng-Fan potential are obtained and discussed. The…
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of…
The analyticity properties of the scattering amplitude for a massive scalar field is reviewed in this article where the spacetime geometry is $R^{3,1}\otimes S^1$ i.e. one spatial dimension is compact. Khuri investigated the analyticity of…
We present an iterative algorithm to compute numerical approximations of the potential for the Schr\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle,…
We consider the case of scattering by several obstacles in $\mathbb{R}^d$ for $d \geq 2$. We establish a relative trace formula for Neumann and transmission boundary conditions analogous to the one obtained in arXiv:2002.07291 for Dirichlet…
A general approach is established for deriving one-shot performance bounds for information-theoretic problems on general alphabets beyond countable alphabets. It is mainly based on the quantization idea and a novel form of "likelihood…
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and…