Adiabatic sweep theorem for three-dimensional dipolar Bose gases

TL;DR

This paper develops a variational theorem for scattering length in 3D dipolar Bose gases, deriving analytical expressions for key properties and extending Tan's sweep theorem to anisotropic dipolar interactions.

Contribution

It introduces a variational theorem for scattering length with dipole interactions and analytically derives properties of dipolar Bose gases, extending Tan's theorem.

Findings

Momentum distribution inversely proportional to q^4 with anisotropic factor

Analytical expressions for static structure factor and pair distribution function

Extension of Tan's adiabatic sweep theorem to dipolar interactions

Abstract

The variational theorem for the scattering length in the presence of the dipole-dipole interaction is developed. The theorem is applied to the spinless dipolar Bose gas in three dimensions. We calculated analytically the long-range tails of the single-particle momentum distribution and static structure factor, and the pair distribution function at short distances. The momentum distribution is inversely proportional to $q^4$ with the anisotropic prefactor. In the absence of the dipole-dipole interaction, Tan's adiabatic sweep theorem is reproduced as a particular case. For the homogeneous dilute Bose gas, all the relations are calculated analytically.