Abstract
We study the asymptotic behavior of the charge fluctuations 〈(Q Λ − 〈(Q Λ〉)2〉 in infinite classical systems of charged particles, and show, under certain clustering assumptions, that if the charge fluctuations are not extensive, then they are necessarily of the order of the surface ¦∂λ¦. Moreover, when the canonical sum rules that are typical for equilibrium states of particles interacting with long-range forces hold true, we prove a central limit theorem for the normalized charge variable ¦∂λ¦−1/2(〈(Q Λ − 〈(Q Λ〉)) in two and three dimensions. In one dimension, the probability distribution of the charge itself converges. The latter case is illustrated by the example of the one-dimensional Coulomb gas.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ch. Gruber, Ch. Lugrin, and Ph. A. Martin, Equilibrium properties of classical systems with long range forces, BBGKY equation, neutrality, screening, and sum rules, EPFL preprint,J. Stat. Phys. 22:193 (1980).
S. F. Edwards and A. Lenard,J. Math. Phys. 3:778 (1962).
E. H. Lieb and J. L. Lebowitz, Lectures on the thermodynamic limit for Coulomb systems, inLecture Notes in Physics, No. 20 (Springer-Verlag, 1973), p. 136.
M. Aizenman and Ph. A. Martin, in preparation.
D. Ruelle,Statistical Mechanics (Benjamin, 1969), Chapter 47.
M. Duneau, B. Souillard, and D. Iagolnitzer,Commun. Math. Phys. 31:191 (1973).
Ch. Gruber, Ch. Lugrin, and Ph. A. Martin,Helv. Phys. Acta 51:829 (1978).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Martin, P.A., Yalcin, T. The charge fluctuations in classical Coulomb systems. J Stat Phys 22, 435–463 (1980). https://doi.org/10.1007/BF01012866
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01012866