Bose-Einstein Condensation: Fluctuations and the Grand Canonical Catastrophe 

A. Crisanti Sapienza Università Rome

Recent experimental realization of Bose-Einstein Condensation (BEC) with photons under genuine Grand Canonical conditions has provided the evidence for the simultaneous occurrence of macroscopic fluctuations and phase coherence of the condensate. The consolidate opinion considers the macroscopic fluctuations a pathology of the Grand Canonical Ensemble, referred as the Grand Canonical Catastrophe, and incompatible with the spontaneous symmetry breaking associated with the Bose-Einstein condensation. Using as toy model an uniform ideal gas in a box we show that the Bogoliubov quasi-average construction usually employed to describe the Bose-Einstein Condensation  fails to reproduce the experimental observed broken symmetry state. The observed features requires a different pattern of spontaneous symmetry breaking, characterised by condensation of fluctuations and long-range correlations of the order parameter.