Fluctuations of a hot system of electrons in a static potential

When the fluctuations of the electron density are studied, an interesting quality is the statistical distribution of the hole left by an electron filling one of the states of the system. This distribution is determined here by assuming that the single particle wave functions are frozen. The statistical distribution of the hole is obtained by fixing the occupation of a particular state and then calculating the relaxations of other state occupations within the framework of density functional theory (DFT). Numerical applications of the method are performed for Iron at normal density and various temperatures, in two different systems: a finite one, the Average Atom, and an infinite one, the ion embedded in a plasma. The results presented here show: (1) that the fluctuations originate, as expected, in transfers from/to states near the chemical potential and the continuum: (2) the fluctuations of electrons in loosely bound states and in the continuum are decoupled from inner shells fluctuations; and (3) the higher the fluctuating states and the hotter the system, the more one has to treat a system which is extended to the correlation sphere (''infinite'' system)