Absence of exponential clustering in quantum Coulomb fluids.

Abstract

We show that the quantum corrections to the classical correlations of a Coulomb fluid do not decay exponentially fast for all values of the thermodynamical parameters. Specifically, the ${\ensuremath{\Elzxh}}^{4}$ term in the Wigner-Kirkwood expansion of the equilibrium charge-charge correlations of the quantum one-component plasma is found to decay like \ensuremath{\Vert}r${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}10}$. More generally, using functional integration, we present a diagrammatic representation of the \ensuremath{\Elzxh} expansion of the correlations in a multicomponent fluid with a locally regularized Coulomb potential and Maxwell-Boltzmann statistics. The ${\ensuremath{\Elzxh}}^{2n}$ terms are found to decay algebraically for all n\ensuremath{\ge}2. Furthermore, an analysis of the hierarchy equations for the correlations provides upper bounds that are compatible with the findings of the perturbative expansion. Except for the monopole, all higher-order multipole sum rules do not hold, in general, in the quantum system. This violation of the multipole sum rules as well as the related algebraic tails are due to the intrinsic quantum fluctuations that prevent a perfect organization of the screening clouds. This phenomenon is illustrated in a simpler model where the large-distance correlations between two quantum particles embedded in a classical plasma can be exactly computed.