  For an one-dimensional (1D) momentum conserving system, intensive studies
have shown that generally its heat current autocorrelation function (HCAF)
tends to decay in a power-law manner and results in the breakdown of the
Fourier heat conduction law in the thermodynamic limit. This has been
recognized to be a dominant hydrodynamic effect. Here we show that, instead,
the kinetic effect can be dominant in some cases and leads to the Fourier law.
Usually the HCAF undergoes a fast decaying kinetic stage followed by a long,
slowly decaying hydrodynamic tail. In a finite range of the system size, we
find that whether the system follows the Fourier law depends on whether the
kinetic stage dominates. Our study is illustrated by the 1D diatomic gas model,
with which the HCAF is derived analytically and verified numerically by
molecular dynamics simulations.

Statistical Mechanics