Dynamical scaling of polymerized membranes

Monte Carlo simulations have been performed to analyze the sub-diffusion dynamics of a tagged monomer in self-avoiding polymerized membranes in the flat phase. By decomposing the mean square displacement into the out-of-plane (∥) and the in-plane (τ) components, we obtain good data collapse with two distinctive diffusion exponents 2α_∥ = 0.36 ± 0.01 and 2ατ = 0.21 ± 0.01, and the roughness exponents χ_∥ = 0.6 ±0.05 and χτ = 0.25 ± 0.05, respectively for each component. Their values are consistent with the relation from the rotational symmetry. We derive the generalized Langevin equations to describe the sub-diffusional behaviors of a tagged monomer in the intermediate time regime where the collective effect of internal modes in the membrane dominate the dynamics to produce negative memory kernels with a power law. We also briefly discuss how the long-range hydrodynamic interactions alter the exponents.