Random walks with feedback on fractal lattices.

We study numerically a random walk under the competitive processes of a self-organized feedback coupling, characterized by a strength lambda and an underlying fractal lattice. Whereas a fractal structure favors a subdiffusive behavior, a dynamical feedback leads either to localization in case of an attractive feedback, lambda>0, or to superdiffusion for a repulsive memory strength lambda<0. Under the influence of both processes the dynamical exponent z is changed. For a Sierpinski gasket or a Sierpinski carpet with repulsive feedback coupling we get 2/z=1.04 or 2/z=1.08, respectively. When an attractive feedback is dominant, the system offers localization as in the case of a random walk in regular lattices. The numerical results are strongly supported by analytical studies based on scaling arguments.

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