A Canonical Ensemble Approach to the Fermion/Boson Random Point Processes and Its Applications

We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of the canonical ensemble for a fixed number of particles which obey Bose-Einstein, Fermi-Dirac statistics, respectively, in a finite volume. Focusing on the distribution of positions of the particles, we have point processes of the fixed number of points in a bounded domain. By taking the thermodynamic limit such that the particle density converges to a finite value, the boson/fermion processes are obtained. This argument is a realization of the equivalence of ensembles, since resulting processes are considered to describe a grand canonical ensemble of points. Random point processes corresponding to para-particles of order two are discussed as an application of the formulation. Statistics of a system of composite particles at zero temperature are also considered as a model of determinantal random point processes.

• Publication year

  2005

• Venue

  Communications in Mathematical Physics

• Publication date

  2005-01-21

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1007/s00220-005-1507-2arXiv math-ph/0501053
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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