Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids

摘要

In classical semi-infinite Coulomb fluids, two-point correlation functionsexhibit a slow inverse-power law decay along a uniformly charged wall. In thiswork, we concentrate on the corresponding amplitude function which depends onthe distances of the two points from the wall. Recently [L. \v{S}amaj, J. Stat.Phys. {\bf 161}, 227 (2015)], applying a technique of anticommuting variablesto a 2D system of charged rectilinear wall with "counter-ions only", we deriveda relation between the amplitude function and the density profile which holdsfor any temperature. In this paper, using the M\"obius conformal transformationof particle coordinates in a disc, a new relation between the amplitudefunction and the density profile is found for that model. This enables us toprove, at any temperature, the factorization property of the amplitude functionin point distances from the wall and to express it in terms of the densityprofile. Presupposing the factorization property of the amplitude function andusing specific sum rules for semi-infinite geometries, a relation between theamplitude function of the charge-charge structure function and the chargeprofile is derived for many-component Coulomb fluids in any dimension.