相关论文: Analytic bound on the excess charge for the Hartre…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
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…
We consider the fractional Schr\"odinger equations with focusing Hartree type nonlinearity. When the energy is negative, we use a Glassey's virial type argument to show the finite time blow-up of solutions.
The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
This paper continues the analysis of bound quantum systems started in (T. Yarman, A.L. Kholmetskii and O.V. Missevitch. Going from classical to quantum description of bound charged particles. Part 1: basic concepts and assertions), based on…
We set up a model of an electric charge where the noninvertible metric phase of first order gravity supercedes the point charge singularity in a curved spacetime. A topological interpretation of the electric charge is provided in terms of…
We show, in a borderline case which was not covered before, the validity of nonlinear Calder\'on-Zygmund estimates for a class of non-uniformly elliptic problems driven by double phase energies.
We determine many of the atoms of the algebraic lattices arising in $\mathfrak{q}$-theory of finite semigroups.
We present a new semi-empirical model for calculating electron transport in atomic-scale devices. The model is an extension of the Extended H\"uckel method with a self-consistent Hartree potential. This potential models the effect of an…
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…
Bounds are studied for the maximum number, $N_c$, of electrons that can be bound to $K$ atoms of the total nuclear charge $Z$. It is proved that $N_c < \min\{2Z+1, 1.22Z + 3Z^{1/3}\}$ in Schr\"odinger theory. This improves Lieb's bound $N_c…
We consider the Hamiltonian for a charged particle in a harmonic potential in the presence of a magnetic field. The most symmetric case depends on one parameter, the variation of which leads from a spectrum bounded from below to an…
An extension of the analytical model of Talukder et al (Int. J. Mass Spectrom. 269 (2008) 118) is proposed to estimate electron impact single L- and M-shell ionization cross sections of atoms with incident energy from threshold to…
It is shown that the electrostatic potential of atomic nucleus "seen" by a fast charged projectile at short distances is smeared quantum mechanically due to nucleus motion around the atomic center of inertia. For example, the "positive…
In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper…
We present the key elements of the proof of 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.
This manuscript proves the energy scattering of global solutions to a repulsive fourth-order generalized Hartree equation with non-radial data in the inter-critical regime. This work uses a new approach due to Dodson-Murphy [4] and extends…
High energy beams incident on a fixed target may scatter against atomic electrons. To a first approximation, one can treat these electrons as at rest. For precision experiments, however, it is important to be able to estimate the size of,…
We consider the focusing $5$d Hartree equation, which is $L^2$-supercritical, with finite energy initial data, and investigate the solutions at the mass-energy threshold. We establish the existence of special solutions following the work of…