Equilibrium properties of the Vlasov functional: The generalized Poisson-Boltzmann-Emden equation

François Bavaud

Research output: Contribution to journalArticlepeer-review

Abstract

This article investigates in a systematic way the properties of the classical continuous mean-field theory governed by the generalized Poisson-Boltzmann-Emden equation (x)=A exp[- dy (y)V(x-y)] together with the associated variational problem infop 12 dx dy (x) (y)V(x-y)+kT dx (x) ln (x). Origins of the theory are traced back. Past studies (freezing theories, electrostatic and self-gravitating systems) are relocated in a broader framework. New results concerning the thermodynamic limit, phase transitions, metastability, and the shape of density profiles are provided. In particular, the question of ground states (in relationship to condensation and wetting phenomena) is illustrated by numerous explicit solutions. © 1991 The American Physical Society.

Original languageEnglish
Pages (from-to)129-149
Number of pages21
JournalReviews of Modern Physics
Volume63
Issue number1
DOIs
Publication statusPublished - 1991

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