I giorni venerdì 10 e lunedì 13 giugno il prof. Aldo Procacci del Dipartimento di Matematica, Universidade Federal de Minas Gerais (Brasile) terrà due seminari presso il Dipartimento di Matematica dell'Università di Bologna, pazza Porta S. Donato 5, 40126 Bologna.
Ven. 10 Giu, ore 17:00 aula Seminari VIII Piano
The Mayer series: two explicit expressions for its coefficients and the combinatorial problem.
We derive the (formal) Mayer series of the pressure of a system of classical particles interacting via a pair potential from the standard grand canonical partition function. We give two alternative representations of its coefficients e we discuss the combinatorial problem involved towards the question of its convergence. We conclude the talk by giving a brief review on results obtained and methods proposed , since 1963, to face this combinatorial problem
Lun 13 Giu, ore 15:00 aula Enriques
Convergence of the 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 and Ruelle in 1963 for the Mayer series and by Lebowitz and Penrose in 1964 for the Virial series. To get our results we exploit the tree-graph identity given by Penrose in 1967 using a new partition scheme based on minumum spanning trees.
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