Abstract
We discuss the statistics of Bose-Einstein condensation (BEC) in a canonical ensemble of $N$ noninteracting bosons in terms of a Landau function ${\mathcal{L}}_{N}^{\mathrm{BEC}}(q)$ defined by the logarithm of the probability distribution of the order parameter $q$ for BEC. We also discuss the corresponding Landau function for spontaneous symmetry breaking (SSB), which for finite $N$ should be distinguished from ${\mathcal{L}}_{N}^{\mathrm{BEC}}(q)$. Only for $N\ensuremath{\rightarrow}\ensuremath{\infty}$ BEC and SSB can be described by the same Landau function which depends on the dimensionality and on the form of the external potential in a surprisingly complex manner. For bosons confined by a three-dimensional harmonic trap the Landau function exhibits the usual behavior expected for continuous phase transitions.
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