Related papers: Bound on the excess charge for bosonic systems int…

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…

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 prove that the maximum number $N_c$ of non-relativistic electrons that a nucleus of charge $Z$ can bind is less than $1.22Z+3Z^{1/3}$. This improves Lieb's upper bound $N_c<2Z+1$ [{\it Phys. Rev. A} {\bf 29}, 3018-3028 (1984)] when $Z\ge…

We prove an analytic bound on the excess charge for the Hartree equation in the atomic case.

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…

We propose a relativistic one-parameter Hermitian theory for the Coulomb problem with an electric charge greater than 137. In the non-relativistic limit, the theory becomes identical to the Schr\"odinger-Coulomb problem for all Z. Moreover,…

The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic…

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…

The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, in the framework of non-relativistic quantum mechanics, was accomplished decades ago. This result did not take account of…

We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…

The purpose of this note is to give an elementary derivation of a lower bound on the relativistic Thomas-Fermi-Weizs\"acker-Dirac functional of Thomas-Fermi type and to apply it to get an upper bound on the excess charge of this model.

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum dot -- the maximal number of electrons does not exceed twice the nuclear charge. It result is…

We extend the Kubo-Kishi theorem concerning the charge susceptibility of the Hubbard model in the following way: (i) The electron-photon interaction is taken into account. (ii) Not only on-site but also general Coulomb repulsion is…

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 derive a universal upper bound to the entropy of a charged system. The entropy bound follows from application of the generalized second law of thermodynamics to a gedanken experiment in which an entropy-bearing charged system falls into…

Continuous variable entanglement in a system of two interacting charged scalar mesons is studied. The mesons mutual interaction is mediated by a central symmetric Coulomb potential. We work out the difference between relativistic and…

It was shown in a previous work that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. In this paper, we go further and derive…

The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality.…

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…

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…