LARGE CHARGE FLUCTUATIONS IN CLASSICAL COULOMB-SYSTEMS

The typical fluctuation of the net electric charge Q contained in a su bregion LAMBDA of an infinitely extended equilibrium Coulomb system is expected to grow only as square-root S, where S is the surface area o f LAMBDA. For some cases it has been previously shown that Q/ square-r oot S has a Gaussian distribution as \ LAMBDA \ --> infinity. Here we study the probability law for larger charge fluctuations (large-deviat ion problem). We discuss the case when both \ LAMBDA \ and Q are large , but now with Q of an order larger than square-root S. For a given va lue of Q, the dominant microscopic configurations are assumed to be th ose associated with the formation of a double electrical layer along t he surface of LAMBDA. The probability law for Q is then determined by the free energy of the double electrical layer. In the case of a one-c omponent plasma, this free energy can be computed, for large enough Q, by macroscopic electrostatics. There are solvable two-dimensional mod els for which exact microscopic calculations can be done, providing mo re complete results in these cases. A variety of behaviors of the prob ability law are exhibited.