The Anomalous Thermal Conductivity of Quasi-one-dimensional Hard Disks

We confirm that the conduction of heat in a system of quasi-one-dimension hard disks, with mechanically connected heat reservoirs of different temperatures, is anomalous. We consider systems of different sizes at the same density with the same externally applied temperature gradient and observe that the anomalous behaviour changes with system size. For systems with less than 1000 disks we find that the heat flux vector varies with the square root of the number of disks whereas for systems with more than 1000 disks the heat flux vector varies with the 2/3 power of the number of disks.