Dipole and current fluctuations in the quantum one-component plasma at equilibrium

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Abstract
By an analysis of the current and dipole mean square fluctuations per unit volume for a quantum mechanical jellium in thermal equilibrium at temperature beta -1, the authors give a new proof of the sum rule integral dx mod x mod 2S(x)=3/4(h(cross) omega p/ pi ) coth( beta h(cross) omega p/2) for the second moment of the charge-charge correlation function S(x), where omega p is the plasma frequency. No use is made of perturbation theories. The proof relies on correlation inequalities and sum rules which are valid in phases of charged systems having good screening properties. Up to second order in Planck's constant, the current-current correlations have a non-integrable spatial decay even when the corresponding classical state shows Debye screening.

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