Tracer diffusion in cubic lattices

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Abstract
The multivariable Zwanzig-Mori formalism is used to study the tracer diffusion by nearest-neighbor jumps in cubic regular lattices. The effect of the nearest-neighbor correlations has been calculated exactly while the long-range correlations are computed within mode-coupling theory. The agreement between our results and the Monte Carlo results for the tracer correlation factor lies within 3% in the whole concentration range. An alternative method, the continued-fraction expansion of Mori, is also used. It has been shown that for self-diffusion the two-pole approximation is equivalent to the multivariable theory. Furthermore, through the successive steps in the continued-fraction, correlation effects from the first, second, and third steps of the jump of the tracer particle are also estimated.