Energy dissipation in mesoscopic circuits

We will show that energy dissipation in mesoscopic circuits can be included in a consistent manner by the use of a quantum transport formalism developed by the authors. In particular we show how energy dissipation is induced by the presence of elastic scattering barriers. This will enable us to derive the Landauer formula for the conductance of a quantum wire and the Landauer-Buttiker formula for the conductance of a quantum point contact in a consistent way. The derivations of these conductances is realized without referring to so-called reservoirs where all the dissipation is assumed to take place. study of the energy density for a quantum wire containing a localized elastic scattering barrier will clearly show that we are able to investigate the local dissipative properties of mesoscopic systems.