Physics – Mathematical Physics
Scientific paper
2005-01-21
Commun. Math. Phys. 263, 353--380(2006)
Physics
Mathematical Physics
26pages, Some typos are corrected, to be published in Commun. Math. Phys
Scientific paper
10.1007/s00220-005-1507-2
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 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. A statistics of a system of composite particles at zero temperature are also considered as a model of determinantal random point processes.
Ito Keiichi R.
Tamura Hiroyuki
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