Theoretical Aspects of Anomalous Diffusion in Complex Systems

Many relaxation phenomena in the solid phase depend on diffusion, which is usually treated in the framework of statistical methods. Regular diffusion, known as Brownian motion, is characterized by a linear increase of the mean-squared displacement with time. On the other hand, for a whole series of phenomena this simple relation does not hold their temporal evolution of the mean-squared displacement is non-linear and thus obeys at long times  

the mean-squared displacement is a basic characteristic feature for the motion but, as an averaged quantity, it can provide only restricted information about the basic microscopic mechanisms involved. In several works we have also studied the propagator P r,t), the probability to be at r at time t having started at the origin at t = 0. Space limitations prevent us from going into details. Here we focus on (r (t)) and refer to Klafter et al. and Zum-ofen et al. [4, 5] for in-depth analyses of the propagator. 

From the beginning, the role of time-dependent aspects in disordered media has to be emphasized. In usual random walk problems it is often assumed that the disorder is quenched, so that the dynamics evolves over a static substrate, i.e. the geometrical or the energetical disorder is frozen in. However, it is also possible that the dynamical processes are directly under the influence of temporal (possibly medium induced) fluctuations. 

in Section 3.2 we concentrate on photoconductivity, whose canonical description involves the continuous time random walk (CTRW) approach [1, 4, 6 8]. Basic ingredients 

Macromolecular Systems Microsc ic Interactions and Macroscopic Properties Deutsche Fn schungsgemeiiisdiaft (DFG) 

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Theoretical Aspects of Anomalous Diffusion in Complex Systems... 

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