On the physical basis of pattern formation in nonlinear systems

Spatial, respectively spatiotemporal patterns appear in a gaseous conductor (plasma) when an external constraint produces a local gradient of electron kinetic energy. Under such conditions, collective quantum effects related to the spatial separation of the excitation and ionization cross-sections determine the appearance of adjacent opposite space charges. The state of the resulting space charge configuration depends on the self-enhancement process of positive ions production, which destabilizes the system. Thus, a spatial pattern in the form of a stable double layer appears after self-organization when the above gradient is smaller than that for which the double layer transits into a moving phase (spatiotemporal pattern). The proposed explanation, based on investigations performed on self-organization phenomena observed in gaseous conductors, suggests a new possibility to clarify the challenging problems concerning the actual physical basis of pattern formation in semiconductors.