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We consider two complementary polymer strands of length $L$ attached by acommon end monomer. The two strands bind through complementary monomers and atlow temperatures form a double stranded conformation (zipping), while at hightemperature they dissociate (unzipping). This is a simple model of DNA (or RNA)hairpin formation. Here we investigate the dynamics of the strands at theequilibrium critical temperature $T=T_c$ using Monte Carlo Rouse dynamics. Wefind that the dynamics is anomalous, with a characteristic time scaling as$\tau \sim L^{2.26(2)}$, exceeding the Rouse time $\sim L^{2.18}$. Weinvestigate the probability distribution function, the velocity autocorrelationfunction, the survival probability and boundary behaviour of the underlyingstochastic process. These quantities scale as expected from a fractionalBrownian motion with a Hurst exponent $H=0.44(1)$. We discuss similarities anddifferences with unbiased polymer translocation.

Fractional Brownian motion and the critical dynamics of zipping polymers