The canonical and grand-canonical ensembles are two usual marginal cases forultracold Bose gases, but real collections of experimental runs commonly haveintermediate properties. Here we study the continuum of intermediate cases, andlook into the appearance of ensemble equivalence as interaction rises formesoscopic 1d systems. We demonstrate how at sufficient interaction strengththe distributions of condensate and excited atoms become practically identicalregardless of the ensemble used. Importantly, we find that features that arefragile in the ideal gas and appear only in a strict canonical ensemble canbecome robust in all ensembles when interactions become strong. As evidence,the steep cliff in the distribution of the number of excited atoms ispreserved. To make this study, a straightforward approach for generatingcanonical and intermediate classical field ensembles using a modifiedstochastic Gross-Pitaevskii equation (SGPE) is developed.
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