NDLI: General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye--Hückel Regime

Content Provider	Springer Nature Link
Author	Torres, Aldemar Téllez, Gabriel
Copyright Year	2005
Abstract	We study the statistical mechanics of classical Coulomb systems in a low coupling regime (Debye--Hückel regime) in a confined geometry with Dirichlet boundary conditions for the electric potential. We use a method recently developed by the authors which relates the grand partition function of a Coulomb system in a confined geometry with a certain regularization of the determinant of the Laplacian on that geometry with Dirichlet boundary conditions. We study several examples of fully confining geometry in two and three dimensions and semi-confined geometries where the system is confined only in one or two directions of the space. We also generalize the method to study systems confined in arbitrary geometries with smooth boundary. We find a relation between the expansion for small argument of the heat kernel of the Laplacian and the large-size expansion of the grand potential of the Coulomb system. This allow us to find the finite-size expansion of the grand potential of the system in general. We recover known results for the bulk grand potential (in two and three dimensions) and the surface tension (for two-dimensional systems). We find the surface tension for three-dimensional systems. For two-dimensional systems our general calculation of the finite-size expansion gives a proof of the existence a universal logarithmic finite-size correction predicted some time ago, at least in the low coupling regime. For three-dimensional systems we obtain a prediction for the curvature correction to the grand potential of a confined system.
Starting Page	735
Ending Page	765
Page Count	31
File Format	PDF
ISSN	00224715
Journal	Journal of Statistical Physics
Volume Number	118
Issue Number	3-4
e-ISSN	15729613
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2005-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Confined coulomb systems Debye--H\”uckel theory Dirichlet boundary conditions Physical Chemistry Quantum Physics Mathematical and Computational Physics Statistical Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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