Two-dimensional Bose gas at low density

TL;DR

This paper introduces a new theoretical approach to describe low-density Bose gases at zero temperature, deriving ground-state energy expressions for both 2D and 3D systems using irreducible n-point functions.

Contribution

The paper presents a novel method based on wave function decomposition into irreducible n-point functions to analyze low-density Bose gases at zero temperature.

Findings

Reproduces known 3D ground-state energy corrections.

Derives leading-order ground-state energy for 2D Bose gas.

Provides a new theoretical framework for dilute Bose gases.

Abstract

We propose a new method to describe the interacting bose gas at zero temperature. We use the decomposition of the logarithm of the wave function into the irreducible $n$-point functions. We argue that in the low density limit this expansion corresponds to the expansion of the ground-state energy in powers of the small parameter. For three-dimensional system the correction to the ground-state energy in density is reproduced. For two-dimensional dilute bose gas the ground- state energy in the leading order in the parameter $|\ln\a^2\rho|^{-1}$ where $\a$ is a scattering length is obtained.