Ground state energy density of a dilute Bose gas in the canonical transformation

TL;DR

This paper uses a canonical transformation approach to compute higher-order corrections to the ground state energy density and particle depletion in a dilute Bose gas, revealing specific coefficients for the $n a^3$ terms.

Contribution

It introduces a method to calculate higher-order density fluctuation corrections in the ground state energy of a dilute Bose gas.

Findings

Higher-order correction of order $n a^3$ calculated

Coefficients for particle depletion and energy density identified

Method enables more precise analysis of dilute Bose gases

Abstract

A ground state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order $n a^3$ in the particle depletion and ground state energy density of a dilute Bose gas system, which corresponds to the density fluctuation contribution from the excited states. The coefficient of $n a^3$ term is shown to be $2(\pi - 8/3)$ for the particle depletion, and $16(\pi - 8/3)$ for the ground state energy density.