Correlated random walk in lattices: Tracer diffusion at general concentration

A problem of considerable physical interest, wherein a tracer of arbitrary species diffuses against a dynamic background of double occupancy avoiding classical particles of concentration $x$ hopping on regular lattices, is studied. The theory is exact to the leading order in vacancy concentration, $v=1-x$, and to two leading orders in $x$. Moreover, in the intermediate concentration, it incorporates all the dominant fluctuations from the mean field. Results are worked out for a variety of quantities of interest, such as the tracer diffusion coefficient, the dynamic response, as well as the generalized diffusional mass operator for all the Bravais cubic lattices. New insights are obtained regarding the rapid variation of the response and the mass operator near the Brillouin-zone edge as a function of the vacancy concentration when $v\ll 1$. Inversion of the $K$-dependent characteristics of these quantities, not noticed heretofore, is reported and analyzed.