General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime

Details General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime

2004-04-23

arxiv.org/abs/cond-mat/0404588v1

Journal of Statistical Physics 118, 735 (2005)

Physics

Condensed Matter

Statistical Mechanics

26 pages

Scientific paper

10.1007/s10955-004-8827-z

We study the statistical mechanics of classical Coulomb systems in a low coupling regime (Debye-Huckel regime) in a confined geometry with Dirichlet boundary conditions. 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 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 perimeter correction to the grand potential of a confined system.

Affiliated with

Also associated with

No associations

Rating

General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-393471