  We analyze the Rubinstein-Duke model for polymer reptation by means of
density matrix renormalization techniques. We find a crossover behavior for a
series of quantities as function of the polymer length. The crossover length
may become very large if the mobility of end groups is small compared to that
of the internal reptons. Our results offer an explanation to a controversy
between theory, experiments and simulations on the leading and subleading
scaling behavior of the polymer renewal time and diffusion constant.
