In this paper we study the statistics of combinatorial partitions of the integers, which arise when studying the occupation numbers of loops in the mean field Bose gas. We review the results of Lewis and collaborators and get some more precise estimates on the behavior at the critical point (fluctuations of the condensate component, finite volume corrections to the pressure). We then prove limit shape theorems for the loops occupation numbers. In particular we prove that in a certain range of the parameters, a finite fraction of the total mass is, in the limit, supported by infinitely long loops. We also show that this mass is equal to the mass of the condensed state where all particles have zero momentum.

Benfatto, G., Cassandro, M., Merola, I., Presutti, E. (2005). Limit theorems for statistics of combinatorial partitions with applications to mean field Bose gas. JOURNAL OF MATHEMATICAL PHYSICS, 46(3), 1-38 [10.1063/1.1855933].

### Limit theorems for statistics of combinatorial partitions with applications to mean field Bose gas

#### Abstract

In this paper we study the statistics of combinatorial partitions of the integers, which arise when studying the occupation numbers of loops in the mean field Bose gas. We review the results of Lewis and collaborators and get some more precise estimates on the behavior at the critical point (fluctuations of the condensate component, finite volume corrections to the pressure). We then prove limit shape theorems for the loops occupation numbers. In particular we prove that in a certain range of the parameters, a finite fraction of the total mass is, in the limit, supported by infinitely long loops. We also show that this mass is equal to the mass of the condensed state where all particles have zero momentum.
##### Scheda breve Scheda completa Scheda completa (DC)
2005
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - FISICA MATEMATICA
English
Con Impact Factor ISI
Bose condensation; Mean field; Limit theorems; Combinatorial partitions.
Benfatto, G., Cassandro, M., Merola, I., Presutti, E. (2005). Limit theorems for statistics of combinatorial partitions with applications to mean field Bose gas. JOURNAL OF MATHEMATICAL PHYSICS, 46(3), 1-38 [10.1063/1.1855933].
Benfatto, G; Cassandro, M; Merola, I; Presutti, E
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2108/23743`
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