Performance of one-body reduced density matrix functionals for the homogeneous electron gas

The subject of this study is the exchange-correlation-energy functional of reduced density matrix functional theory. Approximations of this functional are tested by applying them to the homogeneous electron gas. We find that two approximations recently proposed by Gritsenko, Pernal, and Baerends, J. Chem. Phys., {\bf 122}, 204102 (2005), yield considerably better correlation energies and momentum distributions than previously known functionals. We introduce modifications to these functionals which, by construction, reproduce the exact correlation energy of the homogeneous electron gas

Luminescence of Apollo 11 and 12 lunar samples

Luminescence of Apollo 11 and 12 rocks measured with UV, X ray, and proton radiatio

Discontinuity of the chemical potential in reduced-density-matrix-functional theory

We present a novel method for calculating the fundamental gap. To this end, reduced-density-matrix-functional theory is generalized to fractional particle number. For each fixed particle number, $M$, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to a function, $E_{\mathrm{tot}}^M$, whose derivative with respect to the particle number has a discontinuity identical to the gap. In contrast to density functional theory, the energy minimum is generally not a stationary point of the total-energy functional. Numerical results, presented for alkali atoms, the LiH molecule, the periodic one-dimensional LiH chain, and solid Ne, are in excellent agreement with CI calculations and/or experimental data.Comment: 9 pages, 3 figures, version as publishe

Open shells in reduced-density-matrix-functional theory

Reduced-density-matrix-functional theory is applied to open-shell systems. We introduce a spin-restricted formulation by appropriately expressing approximate correlation-energy functionals in terms of spin-dependent occupation numbers and spin-independent natural orbitals. We demonstrate that the additional constraint of total-spin conservation is indispensable for the proper treatment of open-shell systems. The formalism is applied to the first-row open-shell atoms. The obtained ground-state energies are in very good agreement with the exact values as well as other state of the art quantum chemistry calculationsComment: 4 pages, 2 figures, corrected typo

Two-pion exchange potential and the πN\pi N amplitude

We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $\pi N$ scattering amplitude which includes $\Delta$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $\pi N$ amplitude satisfies chiral symmetry constraints and fits $\pi N$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the ones used in one-boson-exchange models that fit $NN$ data below the pion production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped tar fil

2D Yang-Mills Theory as a Matrix String Theory

Quantization of two-dimensional Yang-Mills theory on a torus in the gauge where the field strength is diagonal leads to twisted sectors that are completely analogous to the ones that originate long string states in Matrix String Theory. If these sectors are taken into account the partition function is different from the standard one found in the literature and the invariance of the theory under modular transformations of the torus appears to hold in a stronger sense. The twisted sectors are in one-to-one correspondence with the coverings of the torus without branch points, so they define by themselves a string theory. A possible duality between this string theory and the Gross-Taylor string is discussed, and the problems that one encounters in generalizing this approach to interacting strings are pointed out. This talk is based on a previous paper by the same authors, but it contains some new results and a better interpretation of the results already obtained.Comment: 11 pages, LaTeX, 2 figures included with epsf. Talk presented at the 2nd Conference on Quantum aspects of Gauge Theories, Supersymmetry and Unification, Corfu, Greece, 21-26 September 199

Reduced Density Matrix Functional for Many-Electron Systems

Reduced density matrix functional theory for the case of solids is presented and a new exchange correlation functional based on a fractional power of the density matrix is introduced. We show that compared to other functionals, this produces more accurate results for both finite systems. Moreover, it captures the correct band gap behavior for conventional semiconductors as well as strongly correlated Mott insulators, where a gap is obtained in absence of any magnetic ordering.Comment: 4 figs and 1 tabl