Related papers: Relativistic Exchange Bounds
We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial dimensions. In natural units hbar = c = 1 the system has the semirelativistic…
A consistent analysis of relativistic pionic correlations and meson-exchange currents for electroweak quasielastic electron scattering from nuclei is carried out. Fully-relativistic one-pion-exchange electromagnetic operators are developed…
In this paper we study the existence of minimizers for interaction energies with the presence of external potentials. We consider a class of subharmonic interaction potentials, which include the Riesz potentials $|{\bf…
We investigate multipartite entanglement in rings of arbitrary spins with antiferromagnetic interactions between nearest neighbors. In particular, we show that the non-degenerate ground state of rings formed by an even number ($N$) of spins…
We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are H\"older continuous and the free boundary has…
We derive the effective Hamiltonian of the Nonrelativistic Quantum Electrodynamic up to $m\alpha^8$ by using scattering matching approach. At $m\alpha^6$ order, these results are coincide with Pachucki's, which is obtained by applying…
We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct stationary states with non-zero temperature by minimizing the corresponding free…
We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential $J_\gamma(i)=\gamma^2J(\gamma i)$, $J$ with compact support. The system is subject to boundary conditions with vorticity. Using a…
We calculate two-photon exchange amplitudes for the elastic electron-hadron scattering in the nonrelativistic approximation, and obtain analytical formulae for them. Numerical calculations are performed for proton and $^3$He targets.…
We consider the free boundary problem arising from an energy functional which is the sum of a Dirichlet energy and a nonlinear function of either the classical or the fractional perimeter. The main difference with the existing literature is…
The Hartree-Fock equation which is the Euler-Lagrange equation corresponding to the Hartree-Fock energy functional is used in many-electron problems. Since the Hartree-Fock equation is a system of nonlinear eigenvalue problems, the study of…
We perform accurate calculations of the dependence of transition frequencies in two valence electron atoms and ions on a variation of the fine structure constant, alpha. The relativistic Hartree-Fock method is used with many-body…
We numerically study energy spectra and localization properties of the double exchange model at irrational filling factor. To obtain variational ground state, we use a mumerical technique in momentum space by ``embedded'' boundary condition…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
Whereas many different models exist in the mathematical and physics literature for ground states of non-relativistic crystals, the relativistic case has been much less studied and we are not aware of any mathematical result on a fully…
Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the exchange-hole…
We critically reexamine the problem of interatomic exchange interactions, which describe the total energy change caused by infinitesimal rotations of spins near some equilibrium state. For the small variations, such interactions can be…
An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic…
Lorentz's reciprocity lemma and Feld-Tai reciprocity theorem show the effect of interchanging the action and reaction in Maxwell's equations. We derive a free-space version of these reciprocity relations which generalizes the conservation…
Quantum rings can be characterized by a specific radius and ring width. For this rich class of physical systems, an accurate approximation for the exchange-hole potential and thus for the exchange energy is derived from first principles.…