Simple theoretical tools for low dimension Bose gases

TL;DR

This paper introduces simple theoretical tools to analyze low-dimensional Bose gases, focusing on coherence, density fluctuations, and the effects of interactions in 1D, 2D, and 3D systems, including impenetrable bosons.

Contribution

It develops a classical field model, generalizes the Bogoliubov approach, and uses a Fermi gas mapping to study low-dimensional Bose gases with weak interactions.

Findings

Coherence properties and density fluctuations in 1D Bose gases.

Extension of Bogoliubov theory to various dimensions.

Analysis of impenetrable bosons via Fermi gas mapping.

Abstract

We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures larger than the chemical potential. In a second part, using a lattice model for the quantum field, we explain how to carefully generalize the usual Bogoliubov approach to study a degenerate and weakly interacting Bose gas in 1D, 2D or 3D in the regime of weak density fluctuations. In the last part, using the mapping to an ideal Fermi gas in second quantized formalism, we calculate and discuss physically the density fluctuations and the coherence properties of a gas of impenetrable bosons in 1D.