Density Functional Theory of Magnetic Systems Revisited

The Hohenberg-Kohn theorem of density functional theory (DFT) for the case of electrons interacting with an external magnetic field (that couples to spin only) is examined in more detail than previously. A unexpected generalization is obtained: in certain cases (which include half metallic ferromagnets and magnetic insulators) the ground state, and hence the spin density matrix, is invariant for some non-zero range of a shift in uniform magnetic field. In such cases the ground state energy is not a functional of the spin density matrix alone. The energy gap in an insulator or a half metal is shown to be a ground state property of the N-electron system in magnetic DFT.Comment: Four pages, one figure. Submitted for publication, April 13, 2000 Revised, Sept 27, 200

Four-Quark Condensates in Nucleon QCD Sum Rules

The in-medium behavior of the nucleon spectral density including self-energies is revisited within the framework of QCD sum rules. Special emphasis is given to the density dependence of four-quark condensates. A complete catalog of four-quark condensates is presented and relations among them are derived. Generic differences of such four-quark condensates occurring in QCD sum rules for light baryons and light vector mesons are discussed.Comment: Version accepted for publication: corrected typos, minor changes based on referee comments included, reference adde

Spectral averaging techniques for Jacobi matrices

Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under local perturbations

Phase-space density in heavy-ion collisions revisited

We derive the phase space density of bosons from a general boson interferometry formula. We find that the phase space density is connected with the two-particles and the single particle density distribution functions. If the boson density is large, the two particles density distribution function can not be expressed as a product of two single particle density distributions. However, if the boson density is so small that two particles density distribution function can be expressed as a product of two single particle density distributions, then Bertsch's formula is recovered. For a Gaussian model, the effects of multi-particles Bose-Einstein correlations on the mean phase space density are studied.Comment: 18 Pages, Four eps files, EPJC in Pres

T>0 ensemble state density functional theory revisited

A logical foundation of equilibrium state density functional theory in a Kohn-Sham type formulation is presented on the basis of Mermin's treatment of the grand canonical state. it is simpler and more satisfactory compared to the usual derivation of ground state theory, and free of remaining open points of the latter. It may in particular be relevant with respect to cases of spontaneous symmetry breaking like non-collinear magnetism and orbital order.Comment: 7 pages, no figure

The density functional theory of classical fluids revisited

We reconsider the density functional theory of nonuniform classical fluids from the point of view of convex analysis. From the observation that the logarithm of the grand-partition function $\log \Xi [\phi]$ is a convex functional of the external potential $\phi$ it is shown that the Kohn-Sham free energy ${\cal A}[\rho]$ is a convex functional of the density $\rho$. $\log \Xi [\phi]$ and ${\cal A}[\rho]$ constitute a pair of Legendre transforms and each of these functionals can therefore be obtained as the solution of a variational principle. The convexity ensures the unicity of the solution in both cases. The variational principle which gives $\log \Xi [\phi]$ as the maximum of a functional of $\rho$ is precisely that considered in the density functional theory while the dual principle, which gives ${\cal A}[\rho]$ as the maximum of a functional of $\phi$ seems to be a new result.Comment: 10 page