Convergence of Mayer and Virial expansions and the Penrose tree-graph identity

We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose (J Math Phys 4:1312, 1963) and Ruelle (Ann Phys 5:109–120, 1...

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Detalles Bibliográficos
Autores principales: Procacci, A., Yuhjtman, S.A.
Formato: JOUR
Materias:
Classical continuous gas
Mayer series
Tree-graph identities
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03779017_v107_n1_p31_Procacci
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose (J Math Phys 4:1312, 1963) and Ruelle (Ann Phys 5:109–120, 1963) for the Mayer series and by Lebowitz and Penrose (J Math Phys 7:841–847, 1964) for the Virial series. To get our results, we exploit the tree-graph identity given by Penrose (Statistical mechanics: foundations and applications. Benjamin, New York, 1967) using a new partition scheme based on minimum spanning trees. © 2016, Springer Science+Business Media Dordrecht.

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