Mobility Heterogeneity in a 2D Gaussian Lattice Polymer: A Dynamic Monte Carlo Study

We study mobility heterogeneity in a two-dimensional Gaussian lattice polymer using dynamic Monte Carlo simulations. The polymer dynamics is generated from a local three-monomer move dictionary, which explicitly enumerates allowed bond-preserving updates on a square lattice. As a homogeneous benchmark, this dictionary reproduces the expected Rouse-like behavior of an ideal chain, including the crossover in monomer mean-squared displacement (MSD) and the center-of-mass diffusion scaling $D_{\rm cm} \sim N^{-1}$. We then introduce a two-block version of the model in which the two halves of the chain are updated with different attempt rates, $\omega_A$ and $\omega_B$, while the local move dictionary remains unchanged. For $\rho=\omega_A/\omega_B>1$, the more frequently updated block shows a larger block-resolved MSD at early and intermediate times, producing a positive normalized MSD asymmetry. However, numerical measurements show that the center-of-mass diffusion coefficient remains consistent with $D_{\rm cm} \sim N^{-1}$ for all rate ratios studied. We invoke a simple coarse-grained Rouse argument to explain this result analytically. In this minimal Gaussian setting, rate-induced mobility heterogeneity modifies internal relaxation without changing the Rouse scaling of center-of-mass transport.