Related papers: Analytic bound on the excess charge for the Hartre…

We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge Z and the fine structure constant…

We prove an upper bound on the excess charge for non-relativistic atomic systems, independent of the particle statistics. This result improves Lieb's bound of 1984 for any $Z \ge 12$.

We prove the ionization conjecture within the Hartree-Fock theory of atoms. More precisely, we prove that, if the nuclear charge is allowed to tend to infinity, the maximal negative ionization charge and the ionization energy of atoms…

We bound the number of electrons $Q$ that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizs\"acker functional: instead of the classical power $5/3$ more general powers $p$ are…

This paper establishes new bounds on the maximum number of electrons $ N_c(Z) $ that an atom with nuclear charge $Z$ can bind. Specifically, we show that \begin{equation*} N_c(Z) < 1.1185Z + O(Z^{1/3}) \end{equation*} with an explicit bound…

We consider a molecule described by the Hartree-Fock model without the exchange term. We prove that nuclei of total charge $Z$ can bind at most $Z+C$ electrons, where $C$ is a constant independent of $Z$.

In this manuscript, using a technique introduced by P.~T.~Nam in 2012 and the {\it Coulomb Uncertainty Principle}, we prove new bounds on the excess charge for non relativistic atomic systems, independent of the particle statistics. These…

For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…

We prove analytic-type estimates in weighted Sobolev spaces on the eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with singular potentials, which includes the Hartree-Fock equations. Going beyond classical results…

We develop a least-squares method for computing the analytic capacity of compact plane sets with piecewise-analytic boundary. The method furnishes rigorous upper and lower bounds which converge to the true value of the capacity. Several…

We consider an atom described by M\"uller theory, which is similar to Hartree-Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most Z+C electrons, where C is a universal constant. Our proof…

We derive again the upper entropy bound for a charged object by employing thermodynamics of the Kerr-Newman black hole linearised with respect to its electric charge

We give a necessary and sufficient condition for the existence of molecules in M\"uller theory. Furthermore, we show that if a system is stable in Born-Oppenheimer approximation, then the bound on the positive excess charge $ Z-N \le…

We develop an Over Barrier Model for computing charge exchange between ions and one-active-electron atoms at low impact energies. The main feature of the model is the treatment of the barrier crossing process by the electron within a…

We obtain a non--trivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to growth of conjugates classes, estimates of…

The extended Hubbard model in the atomic limit (AL-EHM) on a square lattice with periodic boundary conditions is studied with use of the Monte Carlo (MC) method. Within the grand canonical ensemble the phase and order-order boundaries for…

Assuming hydrogen is charge neutral, CPT invariance demands that antihydrogen also be charge neutral. Quantum anomaly cancellation also demands that antihydrogen be charge neutral. Standard techniques based on measurements of macroscopic…

We establish a C^1,alpha Schauder estimate of a non-standard degenerate elliptic equation and use it to give another proof of the higher order boundary Harnack inequality. As an application, we obtain the analyticity of the free boundary in…

A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-Andr\'e/Harper single-particle models under open boundary conditions is presented here, both…

The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both…