Low-density expansions for the homogeneous dipolar Bose gas at zero temperature

TL;DR

This paper derives low-density analytical expansions for the energy, chemical potential, and correlation functions of a homogeneous dipolar Bose gas at zero temperature, clarifying stability and long-range behavior.

Contribution

It introduces a regularization method for dipole interactions and derives universal low-density expansions within the Bogoliubov framework.

Findings

Leading term proportional to density explains thermodynamic stability.

Analytical long-range asymptotics for correlation functions obtained.

Correction to scattering length derived for small dipolar ranges.

Abstract

The low-density expansions for the energy, chemical potential, and condensate depletion of the homogeneous dilute dipolar Bose gas are obtained by regularizing the dipole-dipole interaction at long distances. It is shown that the leading term, proportional to the density, allows a simple physical interpretation and consistently describes the thermodynamic stability of the system. The long-range asymptotics are obtained analytically for the normal and anomalous one-particle correlation functions and the pair distribution function. We discuss the properties of the two-body scattering with zero relative momentum for the dipole-dipole interaction, in particular, we derive the asymptotics of the wave function and a correction to the scattering length for small values of the dipolar range. We show how the density expansions can be derived within the Bogoliubov model of weakly interacting particles without any divergence from the assumption of universality of the expansions at low densities.