On a variational property of the effective-medium approximation in the theory of liquid metals

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Abstract
It is shown that the effective-medium approximation (EMA) proposed by Roth (1974) to obtain the one-electron Green function of a liquid metal has a simple variational property. The functional which is stationary at the point given by the Green function in the EMA is the integrated density of states (IDOS). Using the variational property, several interesting expressions for the derivatives of the IDOS with respect to some parameters in the theory are obtained in the EMA. The present finding provides the authors with the possibility of evaluating the IDOS accurately without accurate solution of the self-consistency equation in the EMA.