Estudio de Condiciones que Garantizan la N-Representabilidad en la Teoría del Funcional de la Densidad para Temperaturas Finitas en el Ensamble Gran Canónico

Abstract

One of the most important foundation problems within the Density Functional Theory (DFT) is the N-representability of the energy functional. The problem is to find out the conditions that must satisfy the free energy functional expressed as a density functional in order to correspond to the free energy functional expressed in terms of the density matrix of N-particles. This work presents a review of the N-representability problem of the energy functional in the Hohenberg, Kohn and Sham DFT version for pure states and ensembles. A review of the N-representability problem for Finite Temperatures DFT formulation is done. A review of the necessary and sufficient N-representability conditions for 2-matrix and its relationship with the N-representability problema is presented. These results are analized in order to satisfy the N-representability conditions that must achieve the free energy functional in the grand canonical ensemble for Finite Temperatures. Finally the conclussions derived from this study are detailed.