Nonlinear diffusion of vacancies in a crystal

The correlated motion of vacancies breaks the translational symmetry of the jump probability if the concentraton of the vacancies varies from place to place. This leads to a significant deviation from the result of linear diffusion theory. The problem is treated by using the model of a generalized random walk in which the probabilities of a jump by the walker depend on the position.On leave of absence from Department of Applied Science, Faculty of Engineering, Tohoku University, Sendai 980, Japan.