Related papers: Equation satisfied by electron-electron mutual Cou…
Electron density and electron momentum density, while independently tractable experimentally, bear no direct connection without going through the many-electron wave function. However, invoking a variant of the constrained-search formulation…
The combination of density functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is…
Motivated by the considerable importance of material properties in modern condensed matter physics research, and using techniques of the $N_{e}$ -electron systems in terms of the electron density $n_{\sigma e}\left( r\right) $ needed to…
We present here novel insight into exchange-correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the semiclassical limit, the exact…
A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a…
Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation…
It is shown that the Hartree-plus-exchange-correlation density functional potential for an integer N-electron system differs by a constant form the corresponding potential for an (N-1)-electron system if the densities are determined from…
Modern density functional theory (DFT) calculations employ the Kohn-Sham (KS) system of non-interacting electrons as a reference, with all complications buried in the exchange-correlation energy (Exc). The adiabatic connection formula gives…
We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the…
Density Functional Theory relies on universal functionals characteristic of a given system. Those functionals in general are different for the electron gas and for jellium (electron gas with uniform background). However, jellium is…
One approximation is made to describe a M+1 electron many-body wavefunction by a M electron many-body wavefunction and a single electron wavefunction. Under this approximation, we have derived the Coulomb energy which relates the exciton…
We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the…
An exchange-correlation energy functional $ E_{\mathrm xc} $ and the resultant exchange-correlation potential $ v_{\mathrm xc}({\bf r}) $ in density-functional theory are proposed using orbital-dependent coupling-constant-averaged pair…
We study analytically and numerically dynamics and eigenstates of two electrons with Coulomb repulsion on a tight-binding lattice in one and two dimensions. The total energy and momentum of electrons are conserved and we show that for a…
The derivative discontinuity of the exchange-correlation functional of density-functional theory is cast as the difference of two types of electron affinities. We show that standard Kohn-Sham calculations can be used to calculate both…
We show an $\textit{ab initio}$ construction of the energy density functional (EDF) for electron systems using the functional renormalization group. The correlation energies of the homogeneous electron gas given in our framework reproduce…
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in…
Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of…
We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…
We prove that, in the large-dimension limit, the high-density correlation energy $\Ec$ of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by $\Ec \sim -1/(8D^2)$ for any…