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.
https://arxiv.org/abs/1601.03318
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.
answered Oct 15, 2017 at 2:28
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$\begingroup$ Therefore, is not mean-field treatment a good approach? $\endgroup$ Oct 15, 2017 at 2:41
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$\begingroup$ If you are trying to describe these quantum droplets (which I find to be quite interesting) then a mean-field approach will not be good. Maybe there are other features which you can describe using a mean-field approach, but those features are likely less interesting. $\endgroup$ Oct 15, 2017 at 6:28