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Letters in Mathematical Physics

, Volume 108, Issue 2, pp 307–329 | Cite as

Fréchet differentiability of molecular distribution functions II: the Ursell function

  • Martin HankeEmail author
Article

Abstract

For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the thermodynamical limit of the Ursell or pair correlation function. For certain admissible perturbations of the pair potential and sufficiently small activity we rigorously establish Frechet differentiability of the Ursell function in the \(L^1\) norm. Furthermore, concerning the thermodynamical limit of the pair distribution function we explicitly compute its Fréchet derivative as a sum of a multiplication operator and an integral operator.

Keywords

Statistical mechanics Cluster expansion Molecular distribution function Ursell function Radial distribution function Fréchet derivative 

Mathematics Subject Classification

82B21 82B80 

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Institut für MathematikJohannes Gutenberg-Universität MainzMainzGermany

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