  Linear polymers are represented as chains of hopping reptons and their motion
is described as a stochastic process on a lattice. This admittedly crude
approximation still catches essential physics of polymer motion, i.e. the
universal properties as function of polymer length. More than the static
properties, the dynamics depends on the rules of motion. Small changes in the
hopping probabilities can result in different universal behavior. In particular
the cross-over between Rouse dynamics and reptation is controlled by the types
and strength of the hoppings that are allowed. The properties are analyzed
using a calculational scheme based on an analogy with one-dimensional spin
systems. It leads to accurate data for intermediately long polymers. These are
extrapolated to arbitrarily long polymers, by means of finite-size-scaling
analysis. Exponents and cross-over functions for the renewal time and the
diffusion coefficient are discussed for various types of motion.
