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Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids

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Abstract

In classical semi-infinite Coulomb fluids, two-point correlation functions exhibit a slow inverse-power law decay along a uniformly charged wall. In this work, we concentrate on the corresponding amplitude function which depends on the distances of the two points from the wall. Recently Šamaj (J Stat Phys 161:227–249 2015), applying a technique of anticommuting variables to a 2D system of charged rectilinear wall with “counter-ions only”, we derived a relation between the amplitude function and the density profile which holds for any temperature. In this paper, using the Möbius conformal transformation of particle coordinates in a disc, a new relation between the amplitude function and the density profile is found for that model. In all exactly solvable cases, the amplitude function factorizes itself in the two distances from the wall. Presupposing this factorization property at any temperature and using specific sum rules for semi-infinite geometries, a relation between the amplitude function of the charge-charge structure function and the charge profile is derived for many-component Coulomb fluids in any dimension.

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Acknowledgments

The support received from Grant VEGA No. 2/0015/15 is acknowledged.

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  1. Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511, Bratislava, Slovakia

    Ladislav Šamaj

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  1. Ladislav Šamaj
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Correspondence to Ladislav Šamaj.

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Šamaj, L. Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids. J Stat Phys 164, 304–320 (2016). https://doi.org/10.1007/s10955-016-1548-2

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  • DOI: https://doi.org/10.1007/s10955-016-1548-2

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