A Random Point Field related to Bose-Einstein Condensation

TL;DR

This paper derives a mathematical description of the spatial distribution of an ideal boson gas undergoing Bose-Einstein condensation, using advanced point process theory and operator analysis.

Contribution

It introduces a novel point field model for Bose-Einstein condensation, combining two independent point fields via convolution and providing an abstract construction.

Findings

Derived the point field for Bose-Einstein condensate in the thermodynamic limit

Expressed the point field as a convolution of two independent fields

Provided an abstract formulation for the second point field

Abstract

The random point field which describes the position distribution of the system of ideal boson gas in a state of Bose-Einstein condensation is obtained through the thermodynamic limit. The resulting point field is given by convolution of two independent point fields: the so called boson process whose generating functional is represented by inverse of the Fredholm determinant for an operator related to the heat operator and the point field whose generating functional is represented by a resolvent of the operator. The construction of the latter point field in an abstract formulation is also given.