Fractional Brownian motion and the critical dynamics of zipping polymers

Details Fractional Brownian motion and the critical dynamics of zipping polymers Fractional Brownian motion and the critical dynamics of zipping polymers

2011-11-18

arxiv.org/abs/1111.4323v2

Phys. Rev. E 85, 031120 (2012)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 8 figures

Scientific paper

10.1103/PhysRevE.85.031120

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

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