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 equilib
rium, 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.
The Chapter is devoted to reviewing the main features of aging in non disordered systems relaxing via domain growth, after an istantaneous temperature quench. Using the autocorrelation and autoresponse functions to gauge the deviation from equilibriu
m, an hierarchy of processes is obtained by changing the temperature of the quench and the space dimensionality. The special role of the lower critical dimensionality is highlighted. Basic properties like the separation of the time scales and the splitting of degrees of freedom into fast and slow variables are treated in detail, both in general terms and through analytical calculations in solvable models. Though domain growth is believed to be a well understood paradigma of slow relaxation, emphasis of this review is on the non trivial aspects, not yet fully clarified, like the response function scaling behavior.
Condensation of fluctuations is an interesting phenomenon conceptually distinct from condensation on average. One stricking feature is that, contrary to what happens on average, condensation of fluctuations may occurr even in the absence of interacti
on. The explanation emerges from the duality between large deviation events in the given system and typical events in a new and appropriately biased system. This surprising phenomenon is investigated in the context of the Gaussian model, chosen as paradigmatical non interacting system, before and after an istantaneous temperature quench. It is shown that the bias induces a mean-field-like effective interaction responsible of the condensation on average. Phase diagrams, covering both the equilibrium and the off-equilibrium regimes, are derived for observables representative of generic behaviors.
