相关论文: Numerical treatment of interfaces in Quantum Mecha…

In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of "penalty" type for the…

We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…

We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…

We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…

Quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. Here we propose and theoretically investigate a new quantum interferometric scheme based on three-dimensional waveguide devices.…

Obtaining exact solutions to the Schr\"odinger equation in complex quantum systems poses significant challenges. In this context, numerical methods emerge as valuable tools for analyzing such systems. This article proposes a numerical…

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 apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…

In this paper, we develop a numerical scheme to handle interfaces across computational domains in multi-block schemes for the approximation of systems of conservation laws. We are interested in transmitting shock discontinuities without…

A standard way to solve a Schr\"odinger equation is to discreteize the radial coordinates and apply a numerical method for a differential equation, such as the Runge-Kutta method or the Numerov method. Here I employ a discrete basis…

Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics,…

Two numerical methods are developed to reduce the solution of the radial Schr\"odinger equation for proposed heavy quark-antiquark interactions, into the solution of the eigenvalue problem for the infinite system of tridiagonal matrices.…

Computing many eigenpairs of the Schr{\"o}dinger operator presents a computational bottleneck in large-scale quantum simulations due to the global communication overhead of explicit orthogonalization. To address this issue, we propose a…

We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…

In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…

There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…

Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…

The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…

We study a quantum computer with fixed and permanent interaction of diagonal type between qubits. It is controlled only by one-qubit quick transformations. It is shown how to implement Quantum Fourier Transform and to solve Shroedinger…