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Analytic solution is given in the steady state limit for the system of Masterequations describing a random walk on one-dimensional periodic lattices witharbitrary hopping rates containing one mobile, directional impurity (defectbond). Due to the defect, translational invariance is broken, even if all otherrates are identical. The structure of Master equations lead naturally to theintroduction of a new entity, associated with the walker-impurity pair which wecall the quasi-walker. The velocities and diffusion constants for both therandom walker and impurity are given, being simply related to that of thequasi-particle through physically meaningful equations. Applications in drivendiffusive systems are shown, and connections with the Duke-Rubinstein reptationmodels for gel electrophoresis are discussed.Comment: 31 LaTex pages, 5 Postscript figures included, to appear in Journal  of Statistical Physic

Periodic one-dimensional hopping model with one mobile directional impurity