  We study in momentum-conserving systems, how nonintegrable dynamics may
affect thermal transport properties. As illustrating examples, two
one-dimensional (1D) diatomic chains, representing 1D fluids and lattices,
respectively, are numerically investigated. In both models, the two species of
atoms are assigned two different masses and are arranged alternatively. The
systems are nonintegrable unless the mass ratio is one. We find that when the
mass ratio is slightly different from one, the heat conductivity may keep
significantly unchanged over a certain range of the system size and as the mass
ratio tends to one, this range may expand rapidly. These results establish a
new connection between the macroscopic thermal transport properties and the
underlying dynamics.
