Pair density functional theory by means of the correlated wave function

We present a density functional scheme for calculating the pair density (PD) by means of the correlated wave function. This scheme is free from both of problems related to PD functional theory, i.e., (a) the need to constrain the variational principle to $N$-representable PDs and (b) the development of a kinetic energy functional. By using the correlated wave function, the searching region for the ground-state PD is substantially extended as compared with our previous theory[Physica B \textbf{372} (2007), in press]. The variational principle results in the simultaneous equations that yield the best PD beyond the previous theory, not to mention the Hartree-Fock approximation

Arbitrary Choice of Basic Variables in Density Functional Theory. I. Formalism

The Hohenberg-Kohn theorem of the density functional theory is extended by modifying the Levy constrained-search formulation. The new theorem allows us to choose arbitrary physical quantities as the basic variables which determine the ground-state properties of the system. Moreover, the theorem establishes a minimum principle with respect to variations in the chosen basic variables as well as with respect to variations in the density. By using this theorem, the self-consistent single-particle equations are derived. N single-particle orbitals introduced reproduce the basic variables. The validity of the theory is confirmed by the examples where the spin-density or paramagnetic current-density is chosen as one of the basic variables. The resulting single-particle equations coincide with the Kohn-Sham equations of the spin-density functional theory (SDFT) or current-density functional theory (CDFT), respectively. By choosing basic variables appropriate to the system, the present theory can describe the ground-state properties more efficiently than the conventional DFT.Comment: 23 pages, 1 figure, Changed conten

The Weyl tensor two-point function in de Sitter spacetime

We present an expression for the Weyl-Weyl two-point function in de Sitter spacetime, based on a recently calculated covariant graviton two-point function with one gauge parameter. We find that the Weyl-Weyl two-point function falls off with distance like r^{-4}, where r is spacelike coordinate separation between the two points.Comment: 9 pages, no figure

Renormalization Group for Matrix Models with Branching Interactions

We develop a method to obtain the large N renormalization group flows for matrix models of 2 dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one matrix models. We show that it can be generalized to two matrices models and we recover the Ising critical points.Comment: 19 pages, 1 latex2e + 7 eps files, revised version (misprints corrected and a few points made more precise

Density functional scheme for calculating the pair density

The density functional scheme for calculating the pair density is presented by means of the constrained-search technique. The resultant single-particle equation takes the form of the modified Hartree-Fock equation which contains the kinetic contribution of the exchange-correlation energy functional as the correlation potential. The practical form of the kinetic contribution is also proposed with the aid of the scaling relations of the kinetic energy functionals.Comment: 5 page