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Anomalous dynamics has been extensively investigated, especially in modelling energy and charge transfer. In many cases the moving objects have been assumed not to possess internal degrees of freedom. In this work, we present models in which the anomalous dynamics is due to the internal modes of the moving particles; it is expected that such features may be easily determined experimentally through either fluorescent measurements or electronic energy transfer. Depending on the system considered, scaling behavior may show up during certain time scales. Thus the motion of simple polymeric chains in dilute solutions scales; the same holds true for fractal networks, whereas the dynamics for other connected structures, such as small-world networks (SWNs) does not scale. Combining SWNs into larger, more regular structures again leads to scaling at longer times; we display this by embedding SWNs into 2D regular superstructures.

Energy transfer in polymers involves not only steps along the chain but also between sites which are far away along the chain's backbone, but which are near each other in Euclidean space. In the present note we study exciton trapping on polymers, modelled as Gaussian chains. The trapping sites along the chain are fixed, but the chain's conformation in Euclidean space changes according to Orwoll-Stockmeyer dynamics. Our Monte-Carlo simulations show that such structural changes influence trapping strongly, even if they are relatively slow on the time scale of the hopping motion. We explain this based on a semi-quantitative approach, using ideas from renewal theory.

We demonstrate how photophysical processes in restricted geometries such as porous oxides differed from analogous processes in regular systems. We have used forced Rayleigh scattering and direct energy transfer to probe different length scales of the internal pore network.

Many excitation relaxation phenomena in ordered and disordered systems can be modelled by diffusion controlled pseudounimolecular A + B → B and bimolecular A + A → 0 reactions. Here only a few exact results are known and one has, in general, to apply approximate forms. Both for the phenomenological investigation of such exciton processes and for assessing the quality of approximations computer simulations have proved to be useful. In this work we focus on the continuous-time random-walk method (CTRW). A central role in the description of reactions is played by S ( t ), the mean number of distinct sites visited in time t . We exemplify our procedures using Levy walks i.e. systems with coupled spatio-temporal memories. For Levy walks S ( t ) shows as a function of the memory-parameters a very interesting, non-universal, non-monotonic behavior. We compare the findings with those for decoupled CTRWs on regular lattices.

In this work we focus on the evaluation of current flow in disordered media, and center on enhanced diffusion. We use the continuous-time random-walk (CTRW) method with coupled spatial and temporal memories, as exemplified by Levy walks. The recent increase of interest in CTRW was triggered by advances in photoconductivity measurements, which monitor large dynamical ranges; here the CTRW method was very successful in explaining the observed deviations from scaling. Under Levy walk conditions we find a large variety of conductivity behaviors.

We study the relaxation of an excited donor due to energy transfer to acceptors embedded in restricted geometries which model different porous structures. We focus on relaxation within spherical and cylindrical volumes and also within fractals. The relaxation of the donor is expressend in terms of a site density function ρ 0 ( r ). Deviations from the known Forster behavior are observed due to the geometrical restrictions.

We study the incoherent energy transfer in molecular crystals, in which the interactions are due to exchange and multipolar long-range forces. For the triangular, square and hexagonal two-dimensional lattices we determine numerically the number of distinct sites Rn visited in random-walks of n steps; this complements our former results for three-dimensional lattices. From the average and the variance of Rn we evaluate the excitation decay caused by randomly distributed traps.

We study the influence of spatial, temporal and energetical aspects on luminescence decay. The models include geometric fractals, continous-time random walks (CTRW) and ultrametric spaces (UMS).

We investigate energy transfer processes in fractal structures and compare direct donor-acceptor transfer to indirect transfer. For the direct mechanism both exact and approximate expressions for the survival follow which depend on the fractal dimension d . For the indirect case the survival probability is determined from the number of distinct sites visited by the excitation in acceptor-free fractals. We show that the short time behavior and the long time tails of the survival probability are governed by the spectral dimension d. We interpolate between these two limits by introducing a scaling law. Thus, for each transfer mechanism a different fractal dimension is decisive.

In this work we analyze several hierarchical models - continuous-time random walks (CTRW), fractals and also ultrametric spaces - which lead to dispersive behavior for the exciton motion. We show that all these models possess some scaling ingredient (temporal, spatial or energetic) and that the combination of such aspects leads to subordination (i.e. the scaling parameters combine multiplicatively). We furthermore discuss possibilities to differentiate experimentally between the models by monitoring the changes in relaxation brought about by temperature and pressure variations.

We consider the luminescence decay on fractals, and study, in the framework of continuous-time random walks, the interplay of the spatial and temporal aspects. We note that the diffusion coefficients and the decays have distinct long-time behaviors: The decays are bounded from below by the tails of the waiting-time distributions, a fact which can lead to avoided-crossing effects.

We study the relaxation of initially excited molecules due to energy transfer to acceptors embedded in confined spaces and due to interaction with diffusing quenchers. Both models have been recently applied to relaxation in porous systems.

Luminescence measurements are standard in disclosing dispersive transport (sublinear squared displacement vs. time dependence) in disordered media. We analyze theoretical and experimental implications for turbulent (superlinear) transport in fluids.