相关论文: Analytic bound on the excess charge for the Hartre…

We propose a simple approximation scheme to compute the effective charge of highly charged colloids (spherical or cylindrical with infinite length). Within non-linear Poisson-Boltzmann theory, we start from an expression of the effective…

The non-relativistic bosonic ground state is studied for quantum N-body systems with Coulomb interactions, modeling atoms or ions made of N "bosonic point electrons" bound to an atomic point nucleus of Z "electron" charges, treated in…

In this work, the calculation of complexity on atomic systems is considered. In order to unveil the increasing of this statistical magnitude with the atomic number due to the relativistic effects, recently reported in [A. Borgoo, F. De…

General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…

Recently, we derived an improved universal upper bound to the entropy of a charged system $S \leq \pi (2E b-q^2)/ \hbar$. There was, however, some uncertainty in the value of the numerical factor which multiplies the $q^2$ term. In this…

We study a class of Hartree type equations and prove a quantitative blow up rate for their blow up solutions. This is an analogue of the result by Merle and Rapha\"el on 3d NLS.

We propose a method for computing upper bounds for the Heilbronn problem for triangles.

We study the Hartree-Fock model for pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator \sqrt{(pc)^2+(mc^2)^2}-mc^2. We prove the existence of a Hartree-Fock…

We prove an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space.

The transport of excess electrons in liquid argon driven out of equilibrium by an applied electric field is revisited using a multi-term solution of Boltzmann's equation together with ab initio liquid phase cross-sections calculated using…

We study the Hartree model for two electrons with spin, living in the two-dimensional or three-dimensional space with Coulomb interactions and submitted to the potential induced by two nuclei of charge +1. In the limit where the nuclei move…

A rigorous formalism for determining the electric dipole polarizability of a three-hadron bound complex in the case that the system has only one bound (ground) state has been elaborated. On its basis, by applying a model wave function that…

The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold:…

We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a…

In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…

Experimentally it has been known for a long time that the electric charges of the observed particles appear to be quantized. An approach to understanding electric charge quantization that can be used for gauge theories with explicit $U(1)$…

Absolute total cross sections for electron capture between slow, highly charged ions and alkali targets have been recently measured. It is found that these cross sections follow a scaling law with the projectile charge which is different…

We justify WKB analysis for Hartree equation in space dimension at least three, in a regime which is supercritical as far as semiclassical analysis is concerned. The main technical remark is that the nonlinear Hartree term can be considered…

By either performing a Taylor expansion or making a polynomial approximation, the Bethe equation for charged particle stopping power in matter can be integrated analytically to obtain the range of charged particles in the continuous…

A relativistic version of the effective charge model for computation of observable characteristics of multi-electron atoms and ions is developed. A complete and orthogonal Dirac hydrogen basis set, depending on one parameter -- effective…