By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints, we examine the center-of-mass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function

$C_\mathrm{N}(t) \approx \partial _t^2 h_\mathrm{N}(t)/2$
CN(t)t2hN(t)/2⁠, measuring the curvature of the COM mean-square displacement hN(t). We demonstrate that CN(t) ≈ −(RN/TN)2(ρ*/ρ) f(x = t/TN) with N being the chain length (16 ⩽ N ⩽ 8192), RNN1/2 is the typical chain size, TNN2 is the longest chain relaxation time, ρ is the monomer density,
$\rho ^*\approx N/R_\mathrm{N}^d$
is the self-density, and f(x) is a universal function decaying asymptotically as f(x) ∼ x−ω with ω = (d + 2) × α, where α = 1/4 for x ≪ 1 and α = 1/2 for x ≫ 1. We argue that the algebraic decay NCN(t) ∼ −t−5/4 for tTN results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.

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