Cumulant 2-matrix of the high-density electron gas and the density matrix functional theory

摘要

The cumulant 2-matrix x is that partof the two-body reduced density matrix gamma_2,which cannot be reduced to products of the one-body reduced density matrix (1-matrix) gamma.This irreducible part x is calculated perturbatively for the high-density electron gas (EG) in its ground state,such that the pair densities and the interaction energy are correctly reproduced in their high-density limits,which are exactly known and summarized here.From the thus available cumulant 2-matrix the pair density in momentum space can be derived and used for a fluctuation analysis and compared with the analog analysis in position space,where it is concluded that "correlation suppresses fluctuatios".The perturbatively available cumulant 2-matrix x can be used also for the high-density electron gas to start the iterative solution of te Yasuda integral equation of density matrix functional theory (DMFT),which is a nonlinear functional relation between the cumulant 2-matrix x and the 1-matrix gamma recently derived fromthe contracted schrodinger equation approach:x~gamma[gamma].From the perturbatively determined x one can find another functional x[gamma] as an alternative approximation for a DMFT.