相关论文: Accurate calculation of the solutions to the Thoma…
It is shown that the atom-molecule collision problem in the presence of an external electric field can be solved using the total angular momentum representation in the body-fixed coordinated frame, leading to a computationally efficient…
In this work, the paraxial version of Maxwell equations is derived with the use of two Riemann-Silberstein vectors. Exact solutions of these equations are then obtained representing the paraxial electromagnetic fields. These fields satisfy…
Equations of Hammerstein type cover large variety of areas and are of much interest to a wide audience due to the fact that they have applications in numerous areas. Suitable conditions are imposed to obtain a strong convergence result for…
In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…
The shell model Monte Carlo (SMMC) method is a powerful method for calculating exactly (up to statistical errors) thermal observables and statistical properties of atomic nuclei. However, its application has been limited by a sign problem…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, with the self-generated magnetic field, and, in particular, to derive relativistic Scott…
We present numerical calculations of the equation of state for dense matter in high magnetic fields, using a temperature dependent Thomas-Fermi theory with a magnetic field that takes all Landau levels into account. Free energies for atoms…
We report on an original method, due to Majorana, leading to a semi-analytical series solution of the Thomas-Fermi equation, with appropriate boundary conditions, in terms of only one quadrature. We also deduce a general formula for such a…
A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for…
Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient…
Numerical exact diagonalization is the ultimate method of choice in order to discuss static, dynamic, and thermodynamic properties of quantum systems. In this article we consider Heisenberg spin-systems and extend the range of applicability…
Fully numerical mesh solutions of 2D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of atoms and…
We calculate accurate eigenvalues of a bounded oscillator by means of the Riccati--Pad\'e method that is based on a rational approximation to a regularized logarithmic derivative of the wavefunction. Sequences of roots of Hankel…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
Dynamical symmetries of Born-Infeld theory associated with its maximal field strength are encoded in a geometry on the tangent bundle of spacetime manifolds. The resulting extension of general relativity respecting a finite upper bound on…
We describe how to solve simultaneous Pad\'e approximations over a power series ring $K[[x]]$ for a field $K$ using $O~(n^{\omega - 1} d)$ operations in $K$, where $d$ is the sought precision and $n$ is the number of power series to…
We consider two-dimensional (2D) "artificial atoms" confined by an axially symmetric potential $V(\rho)$. Such configurations arise in circular quantum dots and other systems effectively restricted to a 2D layer. Using the semiclassical…
Using exact continuous quantum Monte Carlo techniques, we study the zero and finite temperature properties of a system of harmonically trapped one dimensional spin 1/2 fermions with short range interactions. Motivated by experimental…
Approximations by Trefftz functions are rapidly gaining popularity in the numerical solution of boundary value problems of mathematical physics. By definition, these functions satisfy locally, in weak form, the underlying differential…