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

Abstract

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.

26pages, Some typos are corrected, to be published in Commun. Math. Phys

References in corpus (4)

• Determinantal random point fields
• Canonical Partition Functions for Parastatistical Systems of any order
• Fermion and boson random point processes as particle distributions of infinite free Fermi and Bose gases of finite density
• Grand canonical partition functions for multi level para Fermi systems of any order

Cited by in corpus (6)

• Efficient simulation of the Ginibre point process
• A Random Point Field related to Bose-Einstein Condensation
• Mean-Field Interacting Boson Random Point Fields in Weak Harmonic Traps
• Random Point Fields for Para-Partcles of Any Order
• Large Deviation Principle for Non-Interacting Boson Random Point Processes
• Continuum Percolation and Stochastic Epidemic Models on Poisson and Ginibre Point Processes