The improved Gaussian approximation Calculation of Bogoliubov Mode in One Dimensional Bosonic Gas

TL;DR

This paper employs an improved Gaussian approximation to analyze the Bogoliubov mode in a one-dimensional bosonic gas, achieving results that align well with exact numerical solutions and suggesting potential for higher-dimensional applications.

Contribution

The paper introduces an improved Gaussian approximation method for calculating the Bogoliubov mode in 1D bosonic gases, providing results consistent with Bethe ansatz calculations.

Findings

Achieved a gapless excitation spectrum matching Bethe ansatz results

Validated the improved Gaussian approximation against exact numerical data

Suggested applicability to higher-dimensional systems

Abstract

In this paper, we study the homogeneous one-dimensional bosonic gas interacting via a repulsive contact potential by using the improved Gaussian approximation. We obtain the gapless excitation spectrum of Bogoliubov mode. Our result is in good agreement with the exact numerical calculation based on the Bethe ansatz. We speculate that the improved Gaussian approximation could be a quantitatively good approximation for higher dimensional systems.