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Description of Bose-Einstein condensation (BEC) using grand canonical ensemble results in strongly fluctuating distribution $p(N_0)\sim e^{-N_0(\epsilon_0-\mu)/T}$ of a number of condensate particles $N_0$. Such fluctuations are not observed in atomic BEC, so the problem termed grand canonical fluctuation catastrophe arises. Its solution is to switch to canonical or microcanonical ensemble, which are more suitable from the physical point of view in the case of atomic BEC because the particle number in an atomic cloud is fixed.

Some signatures of this fluctuation catastrophe were recently observed in BEC of photons where particle number is not fixed due to absorption and emission processes.

BEC of excitonic polaritons in optical microcavity seems to correspond to grand canonical ensemble from the physical point of view because there is a reservoir of hot excitons is the system, so the particle number is not fixed. Thus we can expect signatures of the grand canonical fluctuation catastrophe in experiments (for example strong fluctuations of condensate fraction in time). Are these signatures indeed observed in exciton-polaritonic BEC? If not, why the fluctuation catastrophe is absent in this case?

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The paper you have cited is an experimental evidence for the grand-canonical fluctuation catastrophe with photons.

Bose-Einstein condensates of exciton-polarons have been observed experimentally in rare earth compounds [1]. Similar to your example of an optical microcavity, the situation should correspond to a grand canonical ensemble. However, while the BEC shows other expected properties of a superfluid, the fluctuations in number of condensed particles has - to my knowledge - not yet been studied.

[1] P. Wachter, B. Bucher, and J. Malar, Phys. Rev. B 69, 094502

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  • $\begingroup$ Yes, but I ask about grand canonical fluctuation catastrophe in BEC of excitonic polaritons, not photons. Sorry if it was not clearly stated in my question, I have updated it. $\endgroup$ – Alexey Sokolik Jul 4 '17 at 10:25
  • $\begingroup$ I apologize, I misread your question. I have updated my answer. $\endgroup$ – Julian Helfferich Jul 5 '17 at 6:44

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