  It is commonly accepted that in concentrated solutions or melts
high-molecular weight polymers display random-walk conformational properties
without long-range correlations between subsequent bonds. This absence of
memory means, for instance, that the bond-bond correlation function, $P(s)$, of
two bonds separated by $s$ monomers along the chain should exponentially decay
with $s$. Presenting numerical results and theoretical arguments for both
monodisperse chains and self-assembled (essentially Flory size-distributed)
equilibrium polymers we demonstrate that some long-range correlations remain
due to self-interactions of the chains caused by the chain connectivity and the
incompressibility of the melt. Suggesting a profound analogy with the
well-known long-range velocity correlations in liquids we find, for instance,
$P(s)$ to decay algebraically as $s^{-3/2}$. Our study suggests a precise
method for obtaining the statistical segment length \bstar in a computer
experiment.
