  Unconcatenated, unknotted polymer rings in the melt are subject to strong
interactions with neighboring chains due to the presence of topological
constraints. We study this by computer simulation using the bond-fluctuation
algorithm for chains with up to N=512 statistical segments at a volume fraction
\Phi=0.5 and show that rings in the melt are more compact than gaussian chains.
A careful finite size analysis of the average ring size R \propto N^{\nu}
yields an exponent \nu \approx 0.39 \pm 0.03 in agreement with a Flory-like
argument for the topologica interactions. We show (using the same algorithm)
that the dynamics of molten rings is similar to that of linear chains of the
same mass, confirming recent experimental findings. The diffusion constant
varies effectively as D_{N} \propto N^{-1.22(3) and is slightly higher than
that of corresponding linear chains. For the ring sizes considered (up to 256
statistical segments) we find only one characteristic time scale \tau_{ee}
\propto N^{2.0(2); this is shown by the collapse of several mean-square
displacements and correlation functions onto corresponding master curves.
Because of the shrunken state of the chain, this scaling is not compatible with
simple Rouse motion. It applies for all sizes of ring studied and no sign of a
crossover to any entangled regime is found.
