Shannon entropies of atomic structure factors, off-diagonal order and radial correlation

Abstract

Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behaviour of the off-diagonal elements of density matrices with respect to the uncertainty principle and to analyse the effects of radial correlation on off-diagonal order. We show that radial correlation induces off-diagonal order in position space which is characterized by larger entropic values. Radial correlation in momentum space is characterized by smaller entropic values as information is forced into regions closer to the diagonal. Related off-diagonal correlation functions are also discussed.