Random walk in distorted crystal structure

Abstract

The problem of random walk of particles over the lattice points of a crystal is considered. The concepts of characteristic times of jumps are used in writing and finding the exact solution for a time-dependent equation of migration in a one-dimensional structure with an anisotropic probability of jumps and in the presence of concentrated traps. The case of some characteristic values of the particle capture efficiency of the trap is considered. Differences are revealed between the results of microscopic analysis and the corresponding results of macroscopic theories and the character of the approximation to the deductions of these theories are shown. Some results are also found for steady-state migration and for a three-dimensional structure.