The Dilute Bose Gas Revised

TL;DR

This paper introduces a new method to analyze dilute Bose gases with strong interactions, resolving previous thermodynamic inconsistencies and deriving a modified energy expansion that accounts for additional interaction length scales.

Contribution

It proposes a variational approach using the second-order reduced density matrix to treat strongly interacting dilute Bose gases, overcoming prior methodological issues.

Findings

Reproduces the known condensate depletion result.

Derives a new energy expansion including an additional length parameter.

Operates with Lennard-Jones type potentials.

Abstract

The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject. The aim of our paper is to propose a new way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singular potentials of the Lennard-Jones type. The derived expansion of the condensate depletion in powers of the boson density n=N/V reproduces the familiar result, while the expansion for the mean energy per particle is of the new form: E=2\pi \hbar^2 a n/m [1+128/(15 \sqrt{\pi})\sqrt{na^3}(1-5b/8a)+ ...], where a is the scattering length and b>0 stands for one more characteristic length depending on the shape of the interaction potential (in particular, for the hard spheres a=b). All the consideration concerns the zero temperature.