Reptation in a weak driving field

A simplified model of reptation is presented. The Master Equation of the model is systematically solved by expansion in powers of the strength of the driving field. From the explicit form of the probability distribution, exact conclusions can be drawn about the average shape of the polymer, its drift velocity, and the zero field diffusion constant. Correlations between segments of the chain are calculated and turn out to be large, even in the weak driving field limit. The results are compared with simulations of the model.