# Cross-over to quasi-condensation: mean-field theories and beyond

## TL;DR

This paper investigates the transition of a 1D Bose gas from an ideal state to a dense quasi-condensate, comparing mean-field theories with exact and simulation methods to understand the crossover behavior.

## Contribution

It provides a comprehensive comparison of mean-field theories, classical-field simulations, and exact solutions for the 1D Bose gas crossover.

## Key findings

- Mean-field theories approximate the equation of state well.
- Classical-field simulations reproduce the smooth crossover.
- Yang-Yang solution offers accurate benchmarks.

## Abstract

We analyze the cross-over of a homogeneous one-dimensional Bose gas from the ideal gas into the dense quasi-condensate phase. We review a number of mean-field theories, perturbative or self-consistent, and provide accurate evaluations of equation of state, density fluctuations, and correlation functions. A smooth crossover is reproduced by classical-field simulations based on the stochastic Gross-Pitaevskii equation, and the Yang-Yang solution to the one-dimensional Bose gas.