Related papers: Relativistic Exchange Bounds
We establish bounds on the energy of a system of N identical bosons bound by attractive pair potentials and obeying the semirelativistic Salpeter equation. The lower bound is provided by a `reduction', with the aid of Jacobi relative…
We present a new hybrid method to solve the relativistic Hartree-Fock-Roothan equations where the one- and two-electron radial integrals are evaluated numerically by defining the basis functions on a grid. This procedure reduces the…
Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is…
Relativistic Hartree-Fock method together with many-body perturbation theory and configuration interaction techniques are used to calculate relativistic energy shifts for frequencies of the strong electric dipole transitions of C III, C IV,…
New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They…
We show in this note how many electron irreducible representations of the Lorentz group L can be expressed in terms of the sums of Slater determinants and principal minors. In this way the full configuration wave function of quantum…
The Hamilton-Lagrange action principle for Relativistic Schr\"odinger Theory (RST) is converted to a variational principle (with constraints) for the stationary bound states. The groundstate energy is the minimally possible value of the…
An efficient method to compute magnetic exchange interactions in systems with strong correlations is introduced. It is based on a magnetic force theorem which evaluates linear response due to rotations of magnetic moments and uses a novel…
We extend Newton's problem of minimal resistance to the Lorentz-Minkowski space. We derive the functional energy and determine the Euler-Lagrange equation. In contrast to the Euclidean case, this equation is quasilinear elliptic, and thus,…
In this paper we develop a generalized formalism for equilibrium thermodynamic systems when an information is shared between the system and the reservoir. The information results in a correction to the entropy of the system. This extension…
The nonlinear Maxwell Lagrangian preserving both conformal and SO(2) duality-rotation invariance has been introduced very recently. Here, in the context of Einstein's theory of gravity minimally coupled with this nonlinear electrodynamics,…
We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to…
We discuss under what conditions the duality between electric and magnetic fields is a valid symmetry of macroscopic quantum electrodynamics. It is shown that Maxwell's equations in the absence of free charges satisfy duality invariance on…
The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional,…
A new formulation of relativistic classical mechanics allows a revisiting of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical…
A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in…
We study the regularity of minimizers of a two-phase energy functional in periodic media. Our main result is a large scale Lipschitz estimate. We also establish improvement-of-flatness for non-degenerate minimizers, which is a key…
We construct phenomenologically a relativistic particle-particle channel interaction which suits the gap equation for nuclear matter. This is done by introducing a density-independent momentum-cutoff parameter to the relativistic mean field…
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…
We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < \infty$. We first prove the existence of possibly infinitely many…