Number Fluctuation in an interacting trapped gas in one and two dimensions

TL;DR

This paper investigates how interactions in one- and two-dimensional trapped gases remove the divergence in number fluctuations seen in ideal Bose gases at low temperatures, using models mapped to exclusion statistics.

Contribution

It introduces models showing that interactions eliminate number fluctuation divergence in low-dimensional Bose gases, connecting them to Haldane-Wu exclusion statistics.

Findings

Interactions remove divergence in number fluctuations at low T.

Models are mapped to non-interacting particles with exclusion statistics.

Comparison of grand canonical and canonical ensemble results.

Abstract

It is well-known that the number fluctuation in the grand canonical ensemble, which is directly proportional to the compressibility, diverges for an ideal bose gas as T -> 0. We show that this divergence is removed when the atoms interact in one dimension through an inverse square two-body interaction. In two dimensions, similar results are obtained using a self-consistent Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may be mapped on to a system of non-interacting particles obeying the Haldane-Wu exclusion statistics. We also calculate the number fluctuation from the ground state of the gas in these interacting models, and compare the grand canonical results with those obtained from the canonical ensemble.