Sum rule for the pair correlation function

TL;DR

This paper derives a new sum rule for the static pair correlation function, extending the relation between density fluctuations and compressibility, and applies it to various quantum gas models.

Contribution

It introduces a novel sum rule for the pair correlation function and demonstrates its applicability to ideal gases and quantum models.

Findings

Sum rule relates pair correlation to density fluctuations.

Applicable to Bose, Fermi gases, BCS, and Bogoliubov models.

Provides a unified framework for correlation analysis.

Abstract

A sum rule has been derived for the static pair correlation function. This rule is the extension of the well-known equation that relates density fluctuation to compressibility. The obtained sum rule is applied to the Bose and Fermi ideal gases as well as BCS and Bogoliubov's models.