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The European Physical Journal C

, Volume 58, Issue 1, pp 83–110 | Cite as

Multiplicity distributions in canonical and microcanonical statistical ensembles

  • M. HauerEmail author
  • V. V. Begun
  • M. I. Gorenstein
Regular Article - Theoretical Physics

Abstract

The aim of this paper is to introduce a new technique for the calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. A Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace’s asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. A Gram–Charlier expansion additionally allows for the calculation of finite volume corrections. Analytical formulas are presented for the inclusion of resonance decay and finite acceptance effects directly into the partition function of the system. This paper consolidates and extends previously published results of the current investigation into the properties of statistical ensembles.

PACS

24.10.Pa 24.60.Ky 05.30.-d 

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  1. 1.Helmholtz Research SchoolUniversity of FrankfurtFrankfurtGermany
  2. 2.University of Cape TownCape TownSouth Africa
  3. 3.Bogolyubov Institute for Theoretical PhysicsKievUkraine
  4. 4.Frankfurt Institute for Advanced StudiesFrankfurtGermany

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