Related papers: Emulating multi-channel scattering based on the ei…
Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schr\"odinger operators and control theory. We review recent results and announce new ones regarding…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when…
Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious…
A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
In this paper the multicasting of independent parallel Gaussian sources over a binary erasure broadcasted channel is considered. Multiresolution embedded quantizer and layered joint source-channel coding schemes are used in order to serve…
Based on the Lippmann-Schwinger equation approach, a generalized L\"uscher's formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A 2D coupled-channel scattering…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
We consider random flights of point particles inside $n$-dimensional channels of the form $\mathbb{R}^{k} \times \mathbb{B}^{n-k}$, where $\mathbb{B}^{n-k}$ is a ball of radius $r$ in dimension $n-k$. The particle velocities immediately…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
In wavefront shaping, waves are focused through complex media onto one or more target points, and the resulting intensity enhancement is quantified by the enhancement factor. While reproducible enhancement is crucial in experiments, the…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
The maximum deposition eigenchannel provides the largest possible power delivery to a target region inside a diffusive medium by optimizing the incident wavefront of a monochromatic beam. It originates from constructive interference of…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…