Anomalous Heat Conduction in a Di-atomic One-Dimensional Ideal Gas
  We provide firm convincing evidence that the energy transport in a one-dimensional gas of elastically colliding free particles of unequal masses is anomalous, i.e. the Fourier Law does not hold. Our conclusions are based on the analysis of the dependence of the heat current on the number of particles, of the internal temperature profile and on the Green-Kubo formalism. 
Giulio Casati and Tomaz Prosen