Application of Effective Field Theory to Density Functional Theory for Finite Systems PDF Download

Author: Anirban Bhattacharyya
Publisher:
ISBN:
Category : Density functionals
Languages : en
Pages :

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Book Description
Abstract: Density functional theory (DFT) is a tool of many-body physics whose popularity has grown over the years, primarily because it provides a useful balance between accuracy and computational cost, allowing large systems to be treated in a simple self-consistent manner. Effective field theory (EFT) is a framework which allows us to study the low-energy phenomena of a system in a systematic fashion. In this thesis, EFT methods are applied to DFT as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates. When conventional Kohn-Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of the kinetic energy density is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. The EFT framework for DFT is generalized to reconcile these approaches. An effective action approach is used to illustrate how the exact Green's function can be calculated in terms of the Kohn-Sham Green's function. An example based on Skyrme energy functionals shows that single-particle Kohn-Sham spectra can be improved by adding sources used to construct the energy functional. Finally, spin-orbit interactions are incorporated in the formalism leading to an energy functional having the same form as that of the Skyrme functional. Gradient expansions in terms of the local Fermi momentum are also worked out, which will be of use in the immediate future.