Anomalous conductivity: impact of nonlinearity and disorder

We reveal the intricate impact of nonlinearity and disorder on the thermal conductivity of acoustic chains. Disorder induces mobility edges and allows to control the amount of extended modes which are the ballistic channels for energy transport. Nonlinearity adds a diffusive conductivity channel through interacting localized modes, and controls the contact resistance at the edges. Analytical arguments and numerical results yield several crossovers between dominating heat channels, when varying the system size and the temperature. We demonstrate that the nonlinearity-induced interaction between the modes alters the transport through existing conductivity channels and creates new ones, underpinning the observed phenomena.