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The Asymptotic Time Dependence of the Mean‐Square Displacement of Particles in a Multicomponent Two‐Sublattices One‐Dimensional Alloy
Author(s) -
ElMeshad N.
Publication year - 1992
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221710202
Subject(s) - lambda , mean squared displacement , vacancy defect , limit (mathematics) , square (algebra) , physics , mean square , displacement (psychology) , condensed matter physics , particle (ecology) , alloy , mathematical physics , chemistry , mathematics , quantum mechanics , mathematical analysis , geometry , psychology , oceanography , geology , molecular dynamics , psychotherapist , organic chemistry
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 .