Related papers: Relativistic Exchange Bounds
We study three well known models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativistic: the first uses the kinetic energy (p+eA(x))^2 and the…
The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors.In spite of its importance, there has, to the best of our knowledge, been no…
Recently Mansuripur has called into question the validity of the Lorentz force in connection with relativistic electromagnetic theory. Here we present some very simple point-charge systems treated through order v^{2}/c^{2} in order to…
We study existence, regularity, and qualitative properties of solutions to the system \[ -\Delta u = |v|^{q-1} v\quad \text{ in }\Omega,\qquad -\Delta v = |u|^{p-1} u\quad \text{ in }\Omega,\qquad \partial_\nu u=\partial_\nu v=0\quad \text{…
The leading relativistic and QED corrections to the ground state energy of the three-body system (epe) are calculated numerically using a Hylleraas correlated basis set. The accuracy of the nonrelativistic variational ground state wave…
We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. The latter are implemented by…
We calculate the influence of dynamical exchange effects on the response properties and the static properties of a two-dimensional many-polaron gas. These effects are not manifested in the random-phase approximation which is widely used in…
We study the space of $2\to 2$ scattering amplitudes of neutral Goldstone bosons in four space-time dimensions. We establish universal bounds on the first two non-universal Wilson coefficients of the low energy Effective Field Theory (EFT)…
Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem…
In this paper we initiate the study of maps minimising the energy $$ \int_{D} (|\nabla \u|^2+2|\u|)\ dx. $$ which, due to Lipschitz character of the integrand, gives rise to the singular Euler equations $$ \Delta…
We calculate the exchange energy in two dimensional laterally coupled quantum dots using Heitler-London, Hund-Mullikan and variational methods. We assess the quality of these approximations in zero and finite magnetic fields comparing…
Coincidence scattering of polarized electrons from nuclei with polarization transfer to outgoing nucleons is studied within the context of relativistic mean field theory. Effects introduced by the dynamical enhancement of the lower…
The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface- and nano-science. Here we…
Einstein's famous equation $E_{\rm rest}=mc^2$ for the rest energy of a system with mass $m$ requires that the internal energy of the system be included in $m$. Pursuing this idea using Lagrangian and Hamiltonian dynamics yields a…
We report smooth relativistic Hartree-Fock pseudopotentials (also known as averaged relativistic effective potentials or AREPs) and spin-orbit operators for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely non-local…
In the description of the interaction between electrons beyond the classical Hartree picture, bare exchange often yields a leading contribution. Here we discuss its effect on optical spectra of solids, comparing three different frameworks:…
Nonlinear relativistic ionization phenomena induced by a strong linearly polarized laser field are considered. The starting point is the classical relativistic action for a free electron moving in the electromagnetic field created by a…
We show that the molecular relativistic Thomas-Fermi-Weizs\"acker functional consisting of atoms of atomic numbers $Z_1,...,Z_k$ has a minimizer, if the particle number $N$ is constrained to a number less or equal to the total nuclear…
The effects of spin-orbit coupling on the two-electron spectra in lateral coupled quantum dots are investigated analytically and numerically. It is demonstrated that in the absence of magnetic field the exchange interaction is practically…
The possibility of a modification of special relativity with an invariant energy scale playing the role of a minimum energy is explored. Consistency with the equivalence of different inertial frames is obtained by an appropriate choice of a…