Universal relations in Bose gases with power-law interactions in two and three dimensions

TL;DR

This paper derives universal thermodynamic relations for Bose gases with power-law interactions in 2D and 3D, connecting microscopic interactions to macroscopic properties, applicable to various physical systems.

Contribution

It introduces new universal relations and beyond mean-field expressions for Tan's contact in Bose gases with power-law interactions, extending understanding of these systems.

Findings

Derived universal relations between thermodynamics and pair distribution functions.

Established new connections between chemical potential and potential energy.

Provided expressions relevant for systems like dipoles, Rydberg atoms, and van der Waals gases.

Abstract

We derive universal relations between thermodynamic quantities and the pair distribution function for bosons interacting via power-law interactions in three and two dimensions. We find beyond mean-field expressions for Tan's contact and establish new connections between the chemical potential and potential energy per particle, characteristic of systems with finite-range interactions. The obtained results are relevant for dipoles, quadrupoles, Rydberg atoms, excitons, van der Waals atoms, and other systems in the dilute limit.