  The spatial correlations of entangled polymer dynamics are examined by
molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the
soft nature of topological constraints, the initial spatial decays of
intermediate scattering functions of entangled chains are, to the first
approximation, surprisingly similar to those of an unentangled system in the
functional forms. However, entanglements reveal themselves as a long tail in
the reciprocal-space correlations, implying a weak but persistent dynamic
localization in real space. Comparison with a number of existing theoretical
models of entangled polymers suggests that they cannot fully describe the
spatial correlations revealed by simulations and experiments. In particular,
the strict one-dimensional diffusion idea of the original tube model is shown
to be flawed. The dynamic spatial correlation analysis demonstrated in this
work provides a useful tool for interrogating the dynamics of entangled
polymers. Lastly, the failure of the investigated models to even qualitatively
predict the spatial correlations of collective single-chain density
fluctuations points to a possible critical role of incompressibility in polymer
melt dynamics.
