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

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dc.creatorTamura, H.
dc.creatorIto, K. R.
dc.date2005-01-21
dc.date2006-02-01
dc.date.accessioned2026-07-07T06:38:35Z
dc.date.available2026-07-07T06:38:35Z
dc.descriptionWe 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.
dc.description26pages, Some typos are corrected, to be published in Commun. Math. Phys
dc.identifierhttps://arxiv.org/abs/math-ph/0501053
dc.identifierhttp://arxiv.org/abs/math-ph/0501053
dc.identifierCommun. Math. Phys. 263, 353--380(2006)
dc.identifierdoi:10.1007/s00220-005-1507-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100785
dc.subjectMathematical Physics
dc.subject60G55; 82B21
dc.titleA Canonical Ensemble Approach to the Fermion/Boson Random Point Processes and its Applications
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