Non-local effects in charge and energy transport with dissipative electrodes

Recent advances in nano-thermometry motivate the extension of the Landauer-Büttiker scattering theory as to include the non-local dissipation associated with charge transport. Such a program is implemented by describing the inelastic scattering in the connecting electrodes within an electrostatically self-consistent scheme. The restriction to quasi-one-dimensional geometries, weak excitation and low temperature allows to obtain general expressions of the current density and the dissipated power, valid in different regimes, for the cases of an energy-independent mean-free-path or an energy-independent relaxation-rate. In particular, the dissipation asymmetry at both sides of a nano-device and the conditions for observing heating spots with a local maximum of the dissipated power are formulated in terms of the key parameters that define the nano-device and its environment.