Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

Considering an old and recurrent problem of nonequilibrium statistical physics, namely, the microscopic study of the heat flow, we investigate the effects on the heat conduction due the addition of graded structures or long range interactions in some usual models given by chains of oscillators. We show that the presence of these ingredients may considerably change the behavior of the heat flow with the system size, leading to new and unusual features: for example, the decay rate of the heat flow with the system length is increased in the presence of growing graded masses in a chain with local interactions; and we can observe, upon the inclusion of long range interparticle interactions, both the decline and the subsequent rise of the heat current in the same system by varying its length. Since our description is based on generic microscopic models, we expect to have results with some validity in real materials, and so, with practical application in the building of devices used to control and manipulate the heat flow.