Instabilities and Fluctuations
Self-organizing systems present generally a critical value of the control parameter λc “below -which the system is in the disordered phase (below threshold) and above which the system goes into the ordered phase. The buildup of the ordered phase is triggered by a spontaneous fluctuation. From a mathematical point of view, one notes that the macroscopic dynamic equations for self-organizing systems are intrinsically homogeneous, i.e. ρ = 0 must be a solution (ρ is the order parameter). Therefore if the system is initially at ρ = 0, it stays there forever and no self-organization takes place unless a spontaneous fluctuation is occurring. The fluctuation may be originated by thermal noise, by quantum noise (e.g., from the spontaneous emission of light), or by external disturbances.
KeywordsPump Power Laser Field Random Force Threshold Region Coexistence Curve
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