Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

2000/04/03 by Ladislav Šamaj
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf

published as J. Stat. Phys. 100 (2000) 949-967 · 22 pages

arxiv created 2000/04/03 · arxiv updated 2009/11/30

Abstract

In a Coulomb fluid confined to a domain V, the dielectric susceptibility tensor χ_V depends on the shape of V, even in the thermodynamic V→∞ limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic V-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant Γ= even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of χ_V predicted by macroscopic electrostatics and gives the finite-size correction term to χ_V.

Related

• Two-dimensional Coulomb Systems in a disk with Ideal Dielectric Boundaries
• Density profiles in a classical Coulomb fluid near a dielectric wall. II. Weak-coupling systematic expansions
• Density profiles in a classical Coulomb fluid near a dielectric wall. I. Mean-field scheme
• Coulomb Systems with Ideal Dielectric Boundaries: Free Fermion Point and Universality
• General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye--H�ckel Regime