Heat conduction of the hard point chain at zero pressure

Equilibrium and nonequilibrium studies of a hard point chain are performed under the condition of a vanishing external pressure. If all particles have the same mass, the dynamics is integrable, but the evolution is highly nontrivial. Numerical simulations in fact reveal that the particle velocities (which are integrals of motion) subdiffuse at equilibrium, while they superdiffuse in steady nonequilibrium regimes. This latter behaviour induces an anomalous thermal conductivity similar to that seen in standard ergodic models. The complexity of the dynamics can be traced back to a peculiar property of the hard point chain which acts as a velocity-dependent filter. Finally, an accurate study of a diatomic (ergodic) chain is performed, which reveals that the thermal conductivity diverges as N2/5 with the number N of particles. This analysis confirms the conjecture that one-dimensional systems belong to a different universality class when the thermodynamic pressure vanishes.