相关论文: The ionization conjecture in Thomas-Fermi-Dirac-vo…

The Furstenberg-S\'ark\"ozy theorem asserts that the difference set $E-E$ of a subset $E \subset \mathbb{N}$ with positive upper density intersects the image set of any polynomial $P \in \mathbb{Z}[n]$ for which $P(0)=0$. Furstenberg's…

A point charge is frequently approximated by various charge distributions deriving the Lorentz-Abraham-Dirac (LAD) equation. Here a rigid spherical shell is treated from this point of view. This particular continuum model is excellent to…

We demonstrate that the charge distributions in Hubbard-model representations of transition metal oxide heterojucntions can be described by a Thomas-Fermi theory in which the energy is approximated as the sum of the electrostatic energy and…

Local(multiplicative) effective potential energy theories of electronic structure comprise the transformation of the Schr{\"o}dinger equation for interacting fermi systems to model noninteracting fermi or bose systems whereby the equivalent…

In this paper we investigate the link between classical electrodynamics and the mass-energy equivalence principle, in view of the conclusions reached in ref.[1]. A formula for the radius of a charged particle is derived. The formula…

A regular charge-monopole theory is derived from simple and self-evident postulates. It is shown that this theory provides explanations for effects of strong and nuclear interactions. The theory is compared with Dirac's monopole theory.…

A trace on a C*-algebra is amenable (resp. quasidiagonal) if it admits a net of completely positive, contractive maps into matrix algebras which approximately preserve the trace and are approximately multiplicative in the 2-norm (resp.…

Polarizable atoms interacting with a charged wire do so through an inverse-square potential, $V = - g/r^2$. This system is known to realize scale invariance in a nontrivial way and to be subject to ambiguities associated with the choice of…

We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range…

In view of immense interest to understand impact of an electron on atoms in the low-energy scattering phenomena observed in laboratories and astrophysical processes, we prescribe here an approach to construct potentials using relativistic…

As a natural generalization of the Euler-Mascheroni constant $\gamma$, Y. Ihara introduced the Euler-Kronecker constant $\gamma_K$ attached to any number field $K$. In this paper, we prove that a certain bound on $\gamma_K$ in a tower of…

In this report, the impact of the Casimir effect in the near-nuclear environment on electrons, in particular of the K-shell, is investigated. It has long been known that the experimentally measured binding energies of the inner electrons,…

We develop a theory of superconducting pairing in low-density Strontium titanate due to quadratic coupling of electron density to soft transverse optical phonons. It leads to static attractive potential between electrons which decay length…

New formulas to calculate the nuclear charge radii and the nuclear binding energies have been derived in the framework of an alpha-cluster model. The particular features of the model are two assumptions that the proton-neutron pair…

The existence of Anderson localization, characterized by vanishing diffusion due to strong disorder, has been demonstrated in numerous ways. A systematic approach based on the Anderson quantum model of the Fermi gas in random lattices that…

How does nature hold together protons and neutrons to form the wide variety of complex nuclei in the universe? Describing many-nucleon systems from the fundamental theory of quantum chromodynamics has been the greatest challenge in…

We compute the isotope shifts of the \emph{total} electron binding energy of neutral atoms and singly charged ions up to element $Z=120$, using relativistic Hartree-Fock method including the Breit interaction. Field shift coefficients are…

A linear locally nilpotent derivation of the polynomial algebra $K[X_m]$ in $m$ variables over a field $K$ of characteristic 0 is called a Weitzenb\"ock derivation. It is well known from the classical theorem of Weitzenb\"ock that the…

Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and supercurrent as functions of the doping level and of the pairing…

We consider the problem of $N$ identical fermions interacting via a zero-range attractive potential with a lighter atom in one dimension. Using the few-body approach based on the Skorniakov and Ter-Martirosian equation, we determine the…