Large charge fluctuations in classical Coulomb systems

Abstract

The typical fluctuation of the net electric chargeQ contained in a subregionΛ of an infinitely extended equilibrium Coulomb system is expected to grow only as √S, whereS is the surface area ofΛ. For some cases it has been previously shown thatQ/√S has a Gaussian distribution as ¦Λ¦→∞. Here we study the probability law for larger charge fluctuations (large-deviation problem). We discuss the case when both ¦Λ¦ andQ are large, but now withQ of an order larger than √S. For a given value ofQ, the dominant microscopic configurations are assumed to be those associated with the formation of a double electrical layer along the surface ofΛ. The probability law forQ is then determined by the free energy of the double electrical layer. In the case of a one-component plasma, this free energy can be computed, for large enoughQ, by macroscopic electrostatics. There are solvable two-dimensional models for which exact microscopic calculations can be done, providing more complete results in these cases. A variety of behaviors of the probability law are exhibited.