BROWNIAN-MOTION IN CRYSTALS WITH TOPOLOGICAL DEFECTS

The diffusion behaviour of a Brownian particle in a crystal with rando mly distributed topological defects is analyzed by means of the contin uum theory of defects combined with the theory of diffusion on manifol ds. A path-integral representation of the diffusion process is used fo r the calculation of cumulants of the particle position averaged over a defect ensemble. For a random distribution of disclinations the prob lem of Brownian motion reduces to a known random-drift problem. Depend ing on the properties of the disclination ensemble, this yields variou s types of subdiffusional behaviour. In a random array of parallel scr ew dislocations one finds a normal, but anisotropic, diffusion behavio ur of the mean-square displacement. Moreover, the process turns out to be non-Gaussian, and reveals long-time tails in the higher-order cumu lants.