The Asymptotic Time Dependence of the Mean‐Square Displacement of Particles in a Multicomponent Two‐Sublattices One‐Dimensional Alloy

The mean‐square displacement, 〈r 2 (t)〉, of a labeled particle hopping on a linear two‐sublattice system through a multicomponent dynamic background with vacancy concentration v is calculated in the limit of very long times. Our result is 〈r 2 (t)〉 = (2va 2 /c 1/2 ) (J ∼ t /π), where c is the background particle concentration and J ∼ the collective hopping rate given by \documentclass{article}\pagestyle{empty}\begin{document}$ J^ \sim = \left[{\sum\limits_\lambda {x^\lambda \left({1/J^\lambda + 1/J_\lambda ^T } \right)} } \right]^{ - 1}. $\end{document} Here x λ represents the concentration of the A‐species of atoms whose hopping rate on each sublattice is J λ and across the two sublattices is J   λ T .