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We consider the generalized time-dependent Schr\"odinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a…
In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…
In this paper, we propose some variational formulations with the use of high order impedance boundary condition (HOIBC) to solve the scattering problem. We study the existence and uniqueness of the solution. Then, a discretization of these…
In this work, we present sufficient cancellation conditions for the boundedness of inhomogeneous Calder\'on-Zygmund type operators on local Hardy spaces defined over spaces of homogeneous type in the sense of Coifman & Weiss for $ 0<p\leq 1…
The Schrodinger equation for a particle moving in a square well potential with BenDaniel - Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
We consider the problem of constructing transparent boundary conditions for the time-dependent Schr\"odinger equation with a compactly supported binding potential and, if desired, a spatially uniform, time-dependent electromagnetic vector…
We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From a mathematical point of view, their relationships are described by a certain 2-category associated to an even…
We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner…
Recently the new method of the Cherenkov fields and loss factors of a point-like electron bunch passing through longitudinally homogeneous structures lined with arbitrary slowdown layers was proposed. It was shown that the Cherenkov loss…
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a…
We have carried out axisymmetric numerical simulations of a spatially developing hypersonic boundary layer over a sharp 7$^{\circ{}}$-half-angle cone at $M_\infty=7.5$ inspired by the experimental investigations by Wagner (2015).…
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the…
The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires the numerical treatment of the boundary in a finite simulation domain. For the study of a self-assembled InAs dot embedded in GaAs,…
We consider the diffraction of time-harmonic plane waves by a periodic structure, governed by the Helmholtz equation. Bound states in the continuum (BICs) are quasi-periodic fields that remain $L^{2}$-bounded over one period and occur at…
We analyze Schr\"odinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we…
A free non-relativistic particle moving in two dimensions on a half-plane can be described by self-adjoint Hamiltonians characterized by boundary conditions imposed on the systems. The most general boundary condition is parameterized in…
For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of boundary conditions states that the restriction of a global equilibrium state to a subsystem can be obtained as an integral over equilibrium states of the subsystem…
We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features…
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…