Abstract
The dynamics of the plasma discharge through spontaneous symmetry breaking as double layer Langmuir, anodic patterns etc., is treated by means of the fractal description. Considering that the charge carrier movements take place on fractal curves, the electric charge transport is studied in an extended model of scale relativity. Using the motion equation for the complex speed field for the irrotational movement the generalized Schrödinger equation is obtained, and in the absence of dissipation a generalized Korteweg de Vries type equation is obtained. The process is also analyzed at the microscopic scale, when the electrical conductance increase is controlled by means of the soliton coherence. When the external field exceeds a critical value, the solitons which stocks the energy break down and simultaneously release the energy to the environment. The same mechanism can explain the charge transport in composite materials (e. d. nanostructures). Moreover, some correspondences between the theoretical model and the behaviour of the patterns generated by laser ablation are analyzed. Keywords: fractal space-time, charge transport mechanism, nanostructures, composite materials