Diffusion in media with topological disorder
Rudi Schmitz
Institut für Physik
Johannes Gutenberg University, D-55099 Mainz, Germany
Real crystals contain a vast number of topological defects in the form of edge and screw dislocations. It is analyzed whether and how such defects influence the behavior of a Brownian particle that diffuses freely in the crystal. On large length scales, the defects can be treated in a continuum approximation. An appropriate diffusion equation for the Brownian particle, in the presence of a static distribution of defects, can then be derived by means of differential geometrical methods.
The quantity of main interest is the effective diffusion propagator, obtained upon averaging over suitably chosen, quenched defect ensembles. All cummulants of the position of the Brownian particle can be expressed in terms of this effective diffusion propagator. Following standart field-theoretical methods, the effective diffusion propagator and the cummulants are evaluated from a path-integral representation of the diffusion process.
The results reveal non-gaussian diffusion behavior with long-time tails in the higher-order cummulants.