# Continuum of classical-field ensembles from canonical to grand canonical and the onset of their equivalence

## TL;DR

This paper investigates how interactions in ultracold Bose gases lead to the convergence of canonical and grand-canonical ensembles, revealing robust features and ensemble equivalence at strong interactions in mesoscopic 1D systems.

## Contribution

It introduces a method using a modified stochastic Gross-Pitaevskii equation to generate canonical and intermediate classical field ensembles, exploring ensemble equivalence with interactions.

## Key findings

- Ensemble distributions become identical at sufficient interaction strength.
- Fragile features in ideal gases become robust with strong interactions.
- The modified SGPE effectively generates various classical field ensembles.

## Abstract

The canonical and grand-canonical ensembles are two usual marginal cases for ultracold Bose gases, but real collections of experimental runs commonly have intermediate properties. Here we study the continuum of intermediate cases, and look into the appearance of ensemble equivalence as interaction rises for mesoscopic 1d systems. We demonstrate how at sufficient interaction strength the distributions of condensate and excited atoms become practically identical regardless of the ensemble used. Importantly, we find that features that are fragile in the ideal gas and appear only in a strict canonical ensemble can become robust in all ensembles when interactions become strong. As evidence, the steep cliff in the distribution of the number of excited atoms is preserved. To make this study, a straightforward approach for generating canonical and intermediate classical field ensembles using a modified stochastic Gross-Pitaevskii equation (SGPE) is developed.