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
Publicado: 2017
Materias:
Classical continuous gas
Mayer series
Tree-graph identities
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03779017_v107_n1_p31_Procacci
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
id paper:paper_03779017_v107_n1_p31_Procacci
record_format dspace
spelling paper:paper_03779017_v107_n1_p31_Procacci2023-06-08T15:39:04Z Convergence of Mayer and Virial expansions and the Penrose tree-graph identity Classical continuous gas Mayer series Tree-graph identities 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. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03779017_v107_n1_p31_Procacci http://hdl.handle.net/20.500.12110/paper_03779017_v107_n1_p31_Procacci
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Classical continuous gas
Mayer series
Tree-graph identities
spellingShingle Classical continuous gas
Mayer series
Tree-graph identities
Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
topic_facet Classical continuous gas
Mayer series
Tree-graph identities
description 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.
title Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
title_short Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
title_full Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
title_fullStr Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
title_full_unstemmed Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
title_sort convergence of mayer and virial expansions and the penrose tree-graph identity
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03779017_v107_n1_p31_Procacci
http://hdl.handle.net/20.500.12110/paper_03779017_v107_n1_p31_Procacci
_version_ 1768545331998359552

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