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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1007/bf02806588

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1572-9613

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Fourth Moment Sum Rule for the Charge Correlations

Authors: Angel Alastuey Riccardo Fantoni
Publish Date: 2016/04/01
Volume: 163, Issue: 4, Pages: 887-913
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Abstract

We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge We derive a sum rule for the fourth moment of equilibrium charge correlations Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations The induced particle densities and the resulting induced charge density are then computed within density functional theory where the free energy is expanded in powers of the density gradients The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations which involves the isothermal compressibility as well as suitably defined partial compressibilities The familiar Stillinger–Lovett condition is also recovered as a byproduct of our method suggesting that the fourth moment sum rule should hold in any conducting phase This is explicitly checked in the low density regime within the Abe–Meeron diagrammatical expansions Beyond its own interest the fourthmoment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical pointThis work was presented at the conference in the memory of Bernard Jancovici Institut Henri Poincaré Paris 5 and 6 november 2015 and it is dedicated to him We would also like to thank Michael Fisher for his stimulating interest and useful discussions

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