On Nilcompactifications of Prime Spectra of Commutative Rings

Given a ring R and S one of its ideals, we obtain a compactification of the prime spectrum of S through a mainly algebraic process. We name it the R-nilcompactification of SpecS. We study some categorical properties of this construction.Comment: 12 pages, 8 Tikz figure

Ab initio calculations of the dynamical response of copper

The role of localized $d$-bands in the dynamical response of Cu is investigated, on the basis of {\em ab initio} pseudopotential calculations. The density-response function is evaluated in both the random-phase approximation (RPA) and a time-dependent local-density functional approximation (TDLDA). Our results indicate that in addition to providing a polarizable background which lowers the free-electron plasma frequency, d-electrons are responsible, at higher energies and small momenta, for a double-peak structure in the dynamical structure factor. These results are in agreement with the experimentally determined optical response of copper. We also analyze the dependence of dynamical scattering cross sections on the momentum transfer.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

Exact Kohn-Sham potential of strongly correlated finite systems

The dissociation of molecules, even the most simple hydrogen molecule, cannot be described accurately within density functional theory because none of the currently available functionals accounts for strong on-site correlation. This problem has led to a discussion of properties that the local Kohn-Sham potential has to satisfy in order to correctly describe strongly correlated systems. We derive an analytic expression for this potential at the dissociation limit and show that the numerical calculations for a one-dimensional two electron model system indeed approach and reach this limit. It is shown that the functional form of the potential is universal, i.e. independent of the details of the system.Comment: 17 pages, 3 figures, submitted to JC

Exact Maps in Density Functional Theory for Lattice Models

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to- density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening. We show that for fully decoupled subsystems the intra-system steepening transforms into the well-known inter-system derivative discontinuity. An important conclusion is that for e.g. charge transfer processes between localized fragments within the same system it is not the usual inter-system derivative discontinuity that is missing in common ground-state functionals, but rather the differentiable intra-system steepening that we illustrate in the present work

Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules

Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of non-equilibrium dynamical situations relevant for modeling of photo-chemical/physical processes: field-free evolution of a non-stationary state, resonant local excitation, resonant complete charge-transfer, and evolution under an arbitrary field. Lack of these steps in usual approximations yield inaccurate dynamics, for example predicting faster dynamics and incomplete charge transfer

Inelastic lifetimes of hot electrons in real metals

We report a first-principles description of inelastic lifetimes of excited electrons in real Cu and Al, which we compute, within the GW approximation of many-body theory, from the knowledge of the self-energy of the excited quasiparticle. Our full band-structure calculations indicate that actual lifetimes are the result of a delicate balance between localization, density of states, screening, and Fermi-surface topology. A major contribution from $d$-electrons participating in the screening of electron-electron interactions yields lifetimes of excited electrons in copper that are larger than those of electrons in a free-electron gas with the electron density equal to that of valence ($4s^1$) electrons. In aluminum, a simple metal with no $d$-bands, splitting of the band structure over the Fermi level results in electron lifetimes that are smaller than those of electrons in a free-electron gas.Comment: 4 papes, 2 figures, to appear in Phys. Rev. Let