Periodic one-dimensional hopping model with one mobile directional impurity

Analytic solution is given in the steady-state limitt→∞ for the system of master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile directional impurity (defect bond). Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of master equations leads naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasiwalker. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasiparticle through physically meaningful equations. Applications in driven diffusive systems are shown, and connections with the Duke-Rubinstein reptation models for gel electrophoresis are discussed.