Quantum energy flow in mesoscopic dielectric structures

We investigate the phononic energy-transport properties of mesoscopic, suspended dielectric wins. The Landauer formula for the thermal conductance is derived and its universal aspects discussed. We then determine the variance of the energy current in the presence of a steady-state current flow. In the final part, some initial results are presented concerning the nature of the temperature fluctuations of a mesoscopic electron-gas thermometer due to the absorption and emission of wire phonons. [S0163-1829(99)02707-1].