521 research outputs found

    Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb systems. III Loopwise Expansion

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    We present an exact field theoretical representation of an ionic solution made of charged hard spheres. The action of the field theory is obtained by performing a Hubbard-Stratonovich transform of the configurational Boltzmann factor. It is shown that the Stillinger-Lovett sum rules are satisfied if and only if all the field correlation functions are short range functions. The mean field, Gaussian and two-loops approximations of the theory are derived and discussed. The mean field approximation for the free energy constitutes a rigorous lower bound for the exact free energy, while the mean field pressure is an upper bound. The one-loop order approximation is shown to be identical with the random phase approximation of the theory of liquids. Finally, at the two-loop order and in the pecular case of the restricted primitive model, one recovers results obtained in the framework of the mode expansion theory.Comment: 35 pages, 3 figure

    Toward ab initio density functional theory for nuclei

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    We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional local-density-plus-gradients form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wave-function based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals.Comment: 69 pages, 16 figures, many revisions based on feedback. To appear in Progress in Particle and Nuclear Physic

    Effective action and density functional theory

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    The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator functional of connected Green functions for the density and the photon field, offering systematic approximation schemes. The leading order of the perturbation expansion reproduces the Hartree-Fock equation. A renormalization group motivated method is introduced to turn on the Coulomb interaction gradually and to find corrections to the Hartree-Fock and the Kohn-Sham schemes.Comment: New references and a numerical algorithm added, to appear in Phys. Rev. B. 30 pages, no figure
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