The grand canonical catastrophe as an instance of condensation of fluctuations

Abstract

The so-called grand canonical catastrophe of the density fluctuations in the ideal Bose gas is shown to be a particular instance of the much more general phenomenon of condensation of fluctuations, taking place in a large system, in or out of equilibrium, when a single degree of freedom makes a macroscopic contribution to the fluctuations of an extensive quantity. The pathological character of the "catastrophe" is demystified by emphasizing the connection between experimental conditions and statistical ensembles, as demonstrated by the recent realization of photon condensation under grand canonical conditions.

6 pages, 1 figure

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• Condensation vs Ordering: From the Spherical Models to BEC in the Canonical and Grand Canonical Ensemble
• Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers
• Development and regression of a large fluctuation
• Probability distributions with singularities
• Participation ratio for constraint-driven condensation with superextensive mass
• Conditioned random walks and interaction-driven condensation
• (Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
• Thermodynamics of the Noninteracting Bose Gas in a Two-Dimensional Box
• On the fluctuations of the number of atoms in the condensate
• Condensation of Fluctuations in the Ising Model: a Transition without Spontaneous Symmetry Breaking
• Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement
• Relation between Statics and Dynamics in the Quench of the Ising Model to below the Critical Point
• Generalised Gibbs Ensemble for spherically constrained harmonic models