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Dynamical Renormalization of Polymers in Quenched Disorder: Long-Time Diffusion and Short-Time Anomalies

A single self-repelling polymer chain embedded in (2 < d ⩽ 4)-dimensional space and moving in a quenched short-ranged random potential is analysed with the help of the dynamical renormalization group. The renormalization group flow of the time scale is discussed for the first time. The results allow for the evaluation of the mean-squared displacement of the centre of mass in the limit of weak disorder. In contrast to the linear time dependence of a Markovian process, we find a strong acceleration of the motion on short time scales, represented by some anomalous chain-length-dependent power law. For long times we recover normal diffusion with some drastically reduced chain-length-dependent diffusion coefficient.