Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids II
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- 作者：B. Jancovici and L. ?amaj
- 关键词：Coulomb systems ; dielectric susceptibility ; macroscopic electrostatics ; shape ; dependent thermodynamics ; Debye– ; Hü ; ckel theory
- 刊名：Journal of Statistical Physics
- 出版年：2004
- 出版时间：2004
- 年：2004
- 卷：114
- 期：5/6
- 页码：1211-1234
- 全文大小：350 KB
文摘
For a Coulomb system contained in a domain , the dielectric susceptibility tensor is defined as relating the average polarization in the system to a constant applied electric field, in the linear limit. According to the phenomenological laws of macroscopic electrostatics, depends on the specific shape of the domain . In this paper we derive, using the methods of equilibrium statistical mechanics in both canonical and grand-canonical ensembles, the shape dependence of and the corresponding finite-size corrections to the thermodynamic limit, for a class of general -dimensional (2) Coulomb systems, of ellipsoidal shape, being in the conducting state. The microscopic derivation is based on a general principle: the total force acting on a system in thermal equilibrium is zero. The results are checked in the Debye–Hückel limit. The paper is a generalization of a previous one [L. amaj, J. Stat. Phys.100:949 (2000)], dealing with the special case of a one-component plasma in two dimensions. In that case, the validity of the presented formalism has already been verified at the exactly solvable (dimensionless) coupling =2.