Related papers: Resolving all-order method convergence problems fo…
It is widely believed that classical electromagnetism is either unphysical or inconsistent, owing to pathological behavior when self-force and radiation reaction are non-negligible. We argue that there is no inconsistency as long as it is…
We review a large body of predictions obtained within the framework of relativistic meson theory together with the Dirac-Brueckner-Hartree-Fock approach to nuclear matter and finite nuclei. The success of this method has been largely…
One of the most common problems of scientific applications is computation of the derivative of a function specified by possibly noisy or imprecise experimental data. Application of conventional techniques for numerically calculating…
Two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei are discussed using realistic One-Boson-Exchange potentials. In a first scheme, the effects of…
We demonstrate behaviors of correlation effects in the calculations of atomic properties through two commonly employed many-body methods; namely multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic coupled-cluster (RCC) methods.…
A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real…
The Ablowitz-Ladik equations, hereafter called $AL_+$ and $AL_-$, are distinguished integrable discretizations of respectively the focusing and defocusing nonlinear Schr\"odinger (NLS) equations. In this paper we first study the modulation…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
We address the linear-mode analysis performed near an equilibrium configuration in the fluid rest frame with a dynamical magnetic field perturbed on a constant configuration. We develop a simple and general algorithm for an analytic…
The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…
We derive a multiconfigurational time-dependent Hartree theory for systems with particle conversion. In such systems particles of one kind can convert to another kind and the total number of particles varies in time. The theory thus extends…
This article presents the convergence analysis of a sequence of piecewise constant and piecewise linear functions obtained by the Rothe method to the solution of the first order evolution partial differential inclusion…
The Generalized Riemann Problems (GRP) for nonlinear hyperbolic systems of balance laws in one space dimension are now well-known and can be formulated as follows: Given initial-data which are smooth on two sides of a discontinuity,…
We explore the existence and behaviour of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with $n$ basis functions is rigorously identified as…
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
The one-particle three-dimensional Dirac equation with spherical symmetry is solved for the Hulthen potential. The s-wave relativistic energy spectrum and two-component spinor wavefunctions are obtained analytically. Conforming to the…
For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
We develop new perturbative tools to accurately study radiatively-induced first-order phase transitions. Previous perturbative methods have suffered internal inconsistencies and been unsuccessful in reproducing lattice data, which is often…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
We present a robust, ab initio method for addressing atom-light interactions and apply it to photoionization of argon. We use a close-coupling ansatz constructed on a multi-configurational Hartree-Fock description of localized states and…