Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU)oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two latticesites decays as a power ? of the inverse of their distance. We point out the necessity of distinguishing betweenenergy flows towards or from the reservoirs and those within the system . We show that energy flow between thereservoirs occurs via adirect transfer induced by long-range couplings and a diffusive process through the chain.To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such directtransfer of energy between the reservoir. For 0 ?<1, the direct transfer term dominates, meaning that thesystem can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heatcurrent exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which suchsize is proportional to the system size N, the stationary current is independent on N.For ?>1, heat transportmostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data arecompatible with an anomalous diffusion, possibly with an ?-dependent characteristic exponent.