Is possible to study the dysprosium-BEC only using a mean-field approximation?
I know the beyond mean-field brings new properties to BEC, but is it possible to use only the mean-field approximation?
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You may or may not be aware of this work on quantum droplets in Dysprosium BECs which may directly answer your question.
Here the authors create self-bound "quantum droplets" out of a Dysprosium BEC. The mean-field result is that these droplets should collapse due to attractive interactions. A result of this work is to show that quantum fluctuations, which can only arise in a beyond-mean-field treatment, are responsible for the stabilization of these droplets against collapse.
I'll leave it to you to investigate further details.