Anomalous heat transport in chains of oscillators. Some results.

The description of heat transport from first principles has long challenged researchers. The diffusive behaviour of heat, as dictated by Fourier's law of heat conduction, generally breaks down in low dimensions, yielding anomalous heat transport. We study heat transport in a chain of oscillators perturbed by long-range conservative stochastic noise out of equilibrium. By solving the equations governing the evolution of the covariance matrix in the thermodynamic limit, we derive expressions for the temperature profile and heat flux, and show that the evolution is compatible with a fractional diffusion equation. Then, we consider the possibility of long-range interaction and long-range noise and derive exact expressions for the heat current-current correlations in the thermodynamic limit. We explore the consequences of our results on the behaviour of anomalous heat transport.