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Stochastic lattice models for the dynamics of linear polymers

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.