title: Generalizing the debye-Huckel equation in terms of density functional integral
abstract: We discuss the validity of generalized Debye-Huckel (GDH) equation proposed by Fisher et al. [B. P. Lee and M. E. Fisher, Phys. Rev. Lett. 76, 2906 (1996); Europhys. Lett. 39, 611 (1997); M. N. Tamashiro, Y. Levin, and M. C. Barbosa, Physica A 268, 24 (1999)], from the functional integral point of view. The GDH theory considers fluctuations around prescribed densities of positive and negative charges. Hence, we first formulate a density functional integral expression for the canonical system of Coulomb gas, and also demonstrate that this is a dual form to the sine-Gordon theory. Our formalism reveals the following: (i) The induced charge distribution around supposed density favors not only the cancellation of additional electrostatic potential like the original DH theory, but also the countervailing of chemical potential difference between imposed and equilibrium value. (ii) As a consequence apparent charge, absent in the GDH equation, comes out in our generalized equation. (iii) That is, the GDH equation holds only in special cases.
authors.affiliation: Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan.
authors.initials: H
authors.lastname: Frusawa
authors.initials: R
authors.lastname: Hayakawa