Density and Pair Correlation Function of Confined Identical Particles: the Bose-Einstein Case

TL;DR

This paper calculates the density and pair correlation functions for a system of harmonically interacting bosons in a parabolic trap, analyzing their dependence on temperature and particle number using path integral methods.

Contribution

It introduces a path integral approach to compute correlation functions of confined bosons, covering a full range of temperatures and particle numbers.

Findings

Correlation functions depend on temperature and particle number.

Method applies to harmonically interacting bosons in a confining potential.

Provides detailed static response properties for the Bose-Einstein system.

Abstract

Two basic correlation functions are calculated for a model of $N$ harmonically interacting identical particles in a parabolic potential well. The density and the pair correlation function of the model are investigated for the boson case. The dependence of these static response properties on the complete range of the temperature and of the number of particles is obtained. The calculation technique is based on the path integral approach of symmetrized density matrices for identical particles in a parabolic confining well.